Browsing by Author "Riaz, Muhammad Bilal"

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Citation Count: Rehman, Aziz Ur; Jarad, Fahd; Riaz, Muhammad Bilal (2024). "A FRACTIONAL STUDY OF MHD CASSON FLUID MOTION WITH THERMAL RADIATIVE FLUX AND HEAT INJECTION/SUCTION MECHANISM UNDER RAMPED WALL CONDITION: APPLICATION OF RABOTNOV EXPONENTIAL KERNEL", Acta Mechanica et Automatica, Vol. 18, No. 1, pp. 84-92.
A FRACTIONAL STUDY OF MHD CASSON FLUID MOTION WITH THERMAL RADIATIVE FLUX AND HEAT INJECTION/SUCTION MECHANISM UNDER RAMPED WALL CONDITION: APPLICATION OF RABOTNOV EXPONENTIAL KERNEL
(2024) Rehman, Aziz Ur; Jarad, Fahd; Riaz, Muhammad Bilal; 234808
The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u80. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as α, β, Pr, Q, Gr, M, Nr and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model. © 2024 Sciendo. All rights reserved.
Citation Count: Talib, Imran...et al. (2022). "A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations", Alexandria Engineering Journal, Vol. 61, No. 1, pp. 135-145.
A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
(2022) Talib, Imran; Jarad, Fahd; Mirza, Muhammad Umar; Nawaz, Asma; Riaz, Muhammad Bilal; 234808
In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap (.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Citation Count: Saeed, S.T...et al. (2020). "A Mathematical Study of Natural Convection Flow Through A Channel With Non-Singular Kernels: An Application to Transport Phenomena", Alexandria Engineering Journal.
A Mathematical Study of Natural Convection Flow Through A Channel With Non-Singular Kernels: An Application to Transport Phenomena
(Elsevier B.V., 2020) Saeed, Syed Tauseef; Riaz, Muhammad Bilal; Baleanu, Dumitru; Abro, Kashif Ali; 56389
In this manuscript, we have obtained closed form solution using Laplace transform, inversion algorithm and convolution theorem. The study of mass transfer flow of an incompressible fluid is carried out near vertical channel. Recently, new classes of differential operators have been introduced and recognized to be efficient in capturing processes following the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly differential operators say Atangana-Baleanu (ABC) and Caputo-Fabrizio (CF) to model such flow. This model for temperature, concentration and velocity gradient is presented in dimensionless form. The obtained solutions have been plotted for various values physical parameters like α,Df,Gm,Gr,Sc and Pr on temperature and velocity profile. Our results suggest that for the variation of time the velocity behavior for CF and ABC are reversible. Finally, an incremental value of prandtl number is observed for decrease in the velocity field which reflects the control of thickness of momentum and enlargement of thermal conductivity. Further, dynamical analysis of fluid with memory effect are efficient for ABC as compared to CF. © 2020 Faculty of Engineering, Alexandria University
Citation Count: Arshad, Muhammad Sarmad...et al. (2020). "A Novel 2-Stage Fractional Runge-Kutta Method for a Time-Fractional Logistic Growth Model", Discrete Dynamics in Nature and Society, Vol. 2020.
A Novel 2-Stage Fractional Runge-Kutta Method for a Time-Fractional Logistic Growth Model
(2020) Arshad, Muhammad Sarmad; Baleanu, Dumitru; Riaz, Muhammad Bilal; Abbas, Muhammad; 56389
In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge-Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge-Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.
Citation Count: Ahmad, Shabir;...et.al. (2022). "A numerical study of dengue internal transmission model with fractional piecewise derivative", Results in Physics, Vol.39.
A numerical study of dengue internal transmission model with fractional piecewise derivative
(2022) Ahmad, Shabir; Yassen, Mansour F.; Alam, Mohammad Mahtab; Alkhati, Soliman; Jarad, Fahd; Riaz, Muhammad Bilal; 234808
The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem's approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer.
Citation Count: Jhangeer, Adil;...et.al. (2020). "Construction of traveling waves patterns of (1+n)-dimensional modified Zakharov-Kuznetsov equation in plasma physics", Results in Physics, Vol.19.
Construction of traveling waves patterns of (1+n)-dimensional modified Zakharov-Kuznetsov equation in plasma physics
(2020) Jhangeer, Adil; Munawar, Maham; Riaz, Muhammad Bilal; Baleanu, Dumitru; 56389
In this research, we examine the modified model of (1+n)-dimensional Zakharov-Kuznetsov (ZK) equation, which will be used to analyze the nature of weakly nonlinear traveling waves in the existence of a constant magnetic area in a plasma comprising in cold ions and hot isothermal electrons. The modified Zakharov-Kuznetsov (mZK) equation will have solutions describing the traveling solitary waves, using the extended [Formula Presented]-expansion method and extended direct algebraic method gives way to the mZK equation regulating the transmission of ion dynamics for nonlinear traveling waves in a plasma. The sufficient conditions for the stability and existence of the traveling wave solutions are reported. Semi-dark, rational, and singular solitary wave solutions are computed. Graphical interpretations of certain practical solutions for specific values of parameters have also been available. The research findings reported throughout this evaluation are fresh and from which this model is employed to analyze waves in numerous plasmas, could be valuable and important. Subsequently, there are concluding remarks mentioned.
Citation Count: Riaz, Muhammad Bilal;...et.al. (2022). "Double Diffusive Magneto-Free-Convection Flow of Oldroyd-B Fluid over a Vertical Plate with Heat and Mass Flux", Symmetry, Vol.14, No.2.
Double Diffusive Magneto-Free-Convection Flow of Oldroyd-B Fluid over a Vertical Plate with Heat and Mass Flux
(2022) Riaz, Muhammad Bilal; Rehman, Aziz Ur; Awrejcewicz, Jan; Jarad, Fahd; 234808
The purpose of this research is to analyze the general equations of double diffusive magnetofree convection in an Oldroyd-B fluid flow based on the fundamental symmetry that are presented in non-dimensional form and are applied to a moving heated vertical plate as the boundary layer flow up, with the existence of an external magnetic field that is either moving or fixed consistent with the plate. The thermal transport phenomenon in the presence of constant concentration, coupled with a first order chemical reaction under the exponential heating of the symmetry of fluid flow, is analyzed. The Laplace transform method is applied symmetrically to tackle the non-dimensional partial differential equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid are presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations. Furthermore, some special cases for the movement of the plate are also studied.
Citation Count: Saeed, Syed Tauseef...et al. (2021). "Exact analysis of second grade fluid with generalized boundary conditions", Intelligent Automation and Soft Computing, Vol. 28, No. 2, pp. 547-559.
Exact analysis of second grade fluid with generalized boundary conditions
(2021) Saeed, Syed Tauseef; Riaz, Muhammad Bilal; Baleanu, Dumitru; Akgül, Ali; Husnine, Syed Muhammad; 56389
Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of time dependent generalized boundary conditions. The non-dimensional forms of the governing equations of the model are developed. These are solved by the classical integral (Laplace) transform technique/method with the convolution theorem and closed form solutions are developed for tem-perature, concentration and velocity. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences. The attained results are in good agreement with the published results. Addition-ally, the impact of thermal radiation with the magnetic field is also analyzed. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect. © 2021, Tech Science Press. All rights reserved.
Citation Count: Aziz-Ur, Rehman...et al. (2021). "Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating", Results in Physics, Vol. 26.
Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating
(2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; 56389
The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results. © 2021
Citation Count: Aziz-Ur, Rehman...et al. (2021). "Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating", Results in Physics, Vol. 26.
Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating
(2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; 56389
The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results.
Citation Count: Cao, Yan...et al. (2021). "Extracting novel categories of analytical wave solutions to a nonlinear Schrödinger equation of unstable type", Results in Physics, Vol. 31.
Extracting novel categories of analytical wave solutions to a nonlinear Schrödinger equation of unstable type
(2021) Cao, Yan; Dhahad, Hayder A.; Jarad, Fahd; Sharma, Kamal; Rajhi, Ali A.; El-Shafay, A.S.; Rashidi, Shima; Rezapour, Shahram; Najati, S.A.; Aly, Ayman A; Alghtani, Abdulaziz H.; Riaz, Muhammad Bilal; 234808
Solving partial differential equations has always been one of the significant tools in mathematics for modeling applied phenomena. In this paper, using an efficient analytical technique, exact solutions for the unstable Schrödinger equation are constructed. This type of the Schrödinger equation describes the disturbance of time period in slightly stable and unstable media and manages the instabilities of lossless symmetric two stream plasma and two layer baroclinic. The basis of this method is the generalization of some commonly used methods in the literature. To better demonstrate the results, we perform many numerical simulations corresponding to the solutions. All these solutions are new achievements for this form of the equation that have not been acquired in previous research. As one of the strengths of the article, it can be pointed out that not only is the method very straightforward, but also can be used without the common computational complexities observed in known analytical methods. In addition, during the use of the method, an analytical solution is obtained in terms of familiar elementary functions, which will make their use in practical applications very convenient. On the other hand, the utilized methodology empowers us to handle other types of well-known models. All numerical results and simulations in this article have been obtained using computational packages in Wolfram Mathematica. © 2021 The Authors
Citation Count: Rehman, Aziz Ur;...et.al. (2022). "Fractional Modeling of Viscous Fluid over a Moveable Inclined Plate Subject to Exponential Heating with Singular and Non-Singular Kernels", Mathematical and Computational Applications, Vol.27, No.1.
Fractional Modeling of Viscous Fluid over a Moveable Inclined Plate Subject to Exponential Heating with Singular and Non-Singular Kernels
(2022) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Rehman, Wajeeha; Awrejcewicz, Jan; Baleanu, Dumitru; 56389
In this paper, a new approach to investigating the unsteady natural convection flow of viscous fluid over a moveable inclined plate with exponential heating is carried out. The mathematical modeling is based on fractional treatment of the governing equation subject to the temperature, velocity and concentration field. Innovative definitions of time fractional operators with singular and non-singular kernels have been working on the developed constitutive mass, energy and momentum equations. The fractionalized analytical solutions based on special functions are obtained by using Laplace transform method to tackle the non-dimensional partial differential equations for velocity, mass and energy. Our results propose that by increasing the value of the Schimdth number and Prandtl number the concentration and temperature profiles decreased, respectively. The presence of a Prandtl number increases the thermal conductivity and reflects the control of thickness of momentum. The experimental results for flow features are shown in graphs over a limited period of time for various parameters. Furthermore, some special cases for the movement of the plate are also studied and results are demonstrated graphically via Mathcad-15 software.
Citation Count: Riaz, Muhammad Bilal;...et.al. (2022).
Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative
(2022) Riaz, Muhammad Bilal; Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; 56389
This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa–Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M-fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa–Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., b ¼ 0:1, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders, i.e., b ¼ 0:7 and b ¼ 0:99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.
Citation Count: Rehman, Aziz U. (2022). "Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach", fractal and fractional, Vol.6, No.98, pp.1-20.
Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach
(2022) Rehman, Aziz Ur; Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; 234808
In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as �� , �� , �� , �� , �� , �� , and �� are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.
Citation Count: Iftikha, Nazishr...et al. (2021). "Heat and Mass Transfer of Natural Convective Flow with Slanted Magnetic Field via Fractional Operators", Journal of Applied and Computational Mechanics, Vol. 7, No. 1, pp. 189-212.
Heat and Mass Transfer of Natural Convective Flow with Slanted Magnetic Field via Fractional Operators
(2021) Iftikha, Nazishr; Baleanu, Dumitru; Riaz, Muhammad Bilal; Husnine, Syed Muhammad; 56389
This article explores the MHD natural convective viscous and incompressible fluid flow along with radiation and chemical reaction. The flow is confined to a moving tilted plate under slanted magnetic field with variable temperature in a porous medium. Non-dimensional parameter along Laplace transformation and inversion algorithm are used to investigate the solution of system of dimensionless governing equations. Fractional differential operators namely, Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in Caputo sense (ABC) are used to compare graphical behavior of for velocity, temperature and concentration for emerging parameters. On comparison, it is observed that fractional order model is better in explaining the memory effect as compared to classical model. Velocity showing increasing behavior for fractional parameter whereas there is a decline in temperature, and concentration profiles for. Fluid velocity goes through a decay due to rise in the values of M, Sc and. However, velocity shows a reverse profile for augmented inputs of Kp, Gr and S. Tabular comparison is made for velocity and Nusselt number and Sherwood number for fractional models. © 2020 Published by Shahid Chamran University of Ahvaz
Citation Count: Asgir, Maryam;...et.al. (2022). "Heat Transfer Of Mhd Oldroyd-B Fluid With Ramped Wall Velocity And Temperature In View Of Local And Nonlocal Differential Operators", Fractals, Vol.30, No.5.
Heat Transfer Of Mhd Oldroyd-B Fluid With Ramped Wall Velocity And Temperature In View Of Local And Nonlocal Differential Operators
(2022) Asgir, Maryam; Riaz, Muhammad Bilal; Jarad, Fahd; Zafar, Azhar Ali; 234808
The theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It's brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed
Citation Count: Chunxia Chen;...et.al. (2022). "Impact of Newtonian Heating via Fourier and Fick’s Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel", Symmetry, Vol.17, No.766.
Impact of Newtonian Heating via Fourier and Fick’s Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel
(2022) Chen, Chunxia; Rehman, Aziz Ur; Riaz, Muhammad Bilal; Jarad, Fahd; Sun, Xiang-E; 234808
In this manuscript, a new approach to study the fractionalized Oldroyd-B fluid flow based on the fundamental symmetry is described by critically examining the Prabhakar fractional derivative near an infinitely vertical plate, wall slip condition on temperature along with Newtonian heating effects and constant concentration. The phenomenon has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick’s and Fourier’s law. The fractional model is transfromed into a non-dimentional form by using some suitable quantities and the symmetry of fluid flow is analyzed. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstrations are made to characterize the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, to validate our current results, some limiting models such as fractional and classical fluid models for Maxwell and Newtonian are recovered, in the presence of with/without slip boundary wall conditions. Further, it is observed from the graphs the velocity curves for classical fluid models are relatively higher than fractional fluid models. A comparative analysis between fractional and classical models depicts that the Prabhakar fractional model explains the memory effects more adequately.
Citation Count: Jarad, Fahd;...et.al. (2022). "Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method", Results in Physics, Vol.37.
Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method
(2022) Jarad; Jhangeer, Adil; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Junaid-U, Rehman M.; 234808
This work is focused to analyze the generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) by the Lie symmetry method. GCBS equation has been utilized to explain the wave profiles in soliton theory. GCBSE was constructed by Bogoyavlenskii and Schiff in different ways (explained in the introduction section). With the aid of Lie symmetry analysis, we have computed the symmetry generators of the GCBSE and commutation relation. We observed from the commutator table, translational symmetries make an Abelian algebra. Then by using the theory of Lie, we have discovered the similarity variables, which are used to convert the supposed nonlinear partial differential equation (NLPDE) into a nonlinear ordinary differential equation (NLODE). Using the new auxiliary method (NAM), we have to discover some new wave profiles of GCBSE in the type of few trigonometric functions. These exits some parameters which we give to some suitable values to attain the different diagrams of some obtained solutions. Further, the GCBSE is presented by non-linear self-adjointness, and conserved vectors are discovered corresponding to each generator.
Citation Count: Rehman, Aziz Ur;...et.al. (2022). "Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative", Case Studies in Thermal Engineering, Vol.34.
Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative
(2022) Rehman, Aziz Ur; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Jarad, Fahd; 234808
In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid.
Citation Count: Riaz, Muhammad Bilal...et al. (2021). "Nonlinear self-adjointness, conserved vectors, and traveling wave structures for the kinetics of phase separation dependent on ternary alloys in iron (Fe-Cr-Y (Y = Mo, Cu))", RESULTS IN PHYSICS, Vol. 25.
Nonlinear self-adjointness, conserved vectors, and traveling wave structures for the kinetics of phase separation dependent on ternary alloys in iron (Fe-Cr-Y (Y = Mo, Cu))
(2021) Riaz, Muhammad Bilal; Baleanu, Dumitru; Jhangeer, Adil; Abbas, Naseem; 56389
The present exploration is concerned with fundamental elements corresponding to the phase decomposition in (Fe-Cr-Mo) and (Fe-Cr-Cu) ternary composites. For the ternary composites of iron, we examine the dynamical behavior of the phase separation. The dynamic of this separation is depicted by a model known as the CahnHilliard equation. The nonlinear self-adjointness for the model under consideration is taken into account. The conserved quantities are calculated with the help of the direct method. For each symmetry generator, we have reduced the considered equation into non-linear ordinary differential equations (ODEs). Also, we have computed the optimal system of the equation under study to find the similarity reduction. Also, the traveling wave structures of the Cahn-Hilliard equation are obtained with the modified simple equation (MSE) technique. Moreover, solitary wave structures is exhibited graphically in the form of 3D, 2D and contour plots.