Browsing by Author "Riaz, Muhammad Bilal"
Now showing 1 - 20 of 32
- Results Per Page
- Sort Options
Article Citation - WoS: 23Citation - Scopus: 28Investigation of Wave Solutions and Conservation Laws of Generalized Calogero-Bogoyavlenskii Equation by Group Theoretic Method(Elsevier, 2022) Jarad, Fahd; Jhangeer, Adil; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Junaid-U-Rehman, M.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.Article Citation - WoS: 25Citation - Scopus: 29Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid With Newtonian Heating: Prabhakar Fractional Derivative Approach(Mdpi, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; Rehman, Aziz UrIn 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 alpha, Pr, beta, Sc, Gr, gamma, and Gm 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.Article Citation - WoS: 19Citation - Scopus: 18Numerical Solutions of the Wolbachia Invasive Model Using Levenberg-Marquardt Backpropagation Neural Network Technique(Elsevier, 2023) Javeed, Shumaila; Ahmed, Iftikhar; Baleanu, Dumitru; Riaz, Muhammad Bilal; Sabir, Zulqurnain; Faiz, ZeshanThe current study presents the numerical solutions of the Wolbachia invasive model (WIM) using the neural network Levenberg-Marquardt (NN-LM) backpropagation technique. The dynamics of the Wolbachia model is categorized into four classes, namely Wolbachia-uninfected aquatic mosquitoes (A*n), Wolbachia-uninfected adult female mosquitoes (Fn*), Wolbachia-infected aquatic mosquitoes (A*w), and Wolbachia-infected adult female mosquitoes (F*w). A reference dataset for the proposed NN-LM technique is created by solving the Wolbachia model using the Runge-Kutta (RK) numerical method. The reference dataset is used for validation, training, and testing of the proposed NN-LM technique for three different cases. The obtained numerical results from the proposed neural network technique are compared with the results obtained from the RK method for accuracy, correctness, and efficiency of the designed methodology. The validation of the proposed solution methodology is checked through the mean square error (MSE), error histograms, error plots, regression plots, and fitness plots.Article 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, DumitruThe 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. © 2021Article Citation - WoS: 98Citation - Scopus: 100Quasi-Periodic, Chaotic and Travelling Wave Structures of Modified Gardner Equation(Pergamon-elsevier Science Ltd, 2021) Hussain, Amjad; Junaid-U-Rehman, M.; Baleanu, Dumitru; Riaz, Muhammad Bilal; Jhangeer, AdilIn this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Furthermore, the one-dimensional optimal system of subalgebras is developed by adjoint technique and then we compute the similarity reductions corresponding to each vector field present in the optimal system, with the help of similarity reduction method we have to convert the PDE into the ODE. Some exact explicit solutions of obtained ordinary differential equations were constructed by the power series technique. With the aid of the Galilean transformation, the model is transformed into a planer dynamical system and the bifurcation behaviour is recorded. All practicable types of phase portraits with regard to the parameters of the problem considered are plotted. Meantime, sensitivity is observed by utilizing sensitivity analysis. In addition, the influence of physical parameters is studied by the application of an extrinsic periodic power. With additional perturbed term, quasi-periodic and quasi-periodic-chaotic behaviours is reported. (c) 2021 Elsevier Ltd. All rights reserved.Article Citation - WoS: 18Citation - Scopus: 19A Fractional Study of Generalized Oldroyd-B Fluid With Ramped Conditions Via Local & Non-Local Kernels(de Gruyter Poland Sp Z O O, 2021) Riaz, Muhammad Bilal; Baleanu, Dumitru; Saeed, Syed TauseefConvective 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 Oldroyd-B fluid in the presence of ramped conditions. The new governing equations of MHD Oldroyd-B fluid have been fractionalized by means of singular and non-singular differentiable operators. In order to have an accurate physical significance of imposed conditions on the geometry of Oldroyd-B fluid, the ramped temperature, concentration and velocity are considered. The fractional solutions of temperature, concentration and velocity have been investigated by means of integral transform and inversion algorithm. 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. The classical calculus is 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 the memory effect. Due to this reason, we applied the modern definition of fractional derivatives. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences.Article Citation - WoS: 23Citation - Scopus: 24A Numerical Study of Dengue Internal Transmission Model With Fractional Piecewise Derivative(Elsevier, 2022) Yassen, Mansour F.; Alam, Mohammad Mahtab; Alkhati, Soliman; Jarad, Fahd; Riaz, Muhammad Bilal; Ahmad, ShabirThe 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.Article Citation - WoS: 12Citation - Scopus: 17Thermal and Concentration Diffusion Impacts on Mhd Maxwell Fluid: a Generalized Fourier's and Fick's Perspective(Elsevier, 2022) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Atangana, Abdon; Jarad, Fahd; Awrejcewicz, JanIn this article, a new approach to study the fractionalized Maxwell fluid is described by the Prabhakar fractional derivative near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomena 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 fractionalized model is transfromed into non-dimensional form by using some suitable dimensionless quantities. 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 demonstration are made to characterized the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, for results validation, comparative study among limiting models derived from fractionalized Prabhakar Maxwell fluid such as fractional and classical fluid models for Maxwell and Newtonian are performed. Further, it is observed from the graphs the valocity curves for classical fluid models relatively higher as compared to fractional fluid models, and fractional approach is more realistic and convenient as compared to classical approach.Article Citation - WoS: 11Citation - Scopus: 11A Generalized Operational Matrix of Mixed Partial Derivative Terms With Applications To Multi-Order Fractional Partial Differential Equations(Elsevier, 2022) Jarad, Fahd; Mirza, Muhammad Umar; Nawaz, Asma; Riaz, Muhammad Bilal; Talib, ImranIn 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.Article Citation - WoS: 10Citation - Scopus: 10Exact Analysis of Second Grade Fluid With Generalized Boundary Conditions(Tech Science Press, 2021) Riaz, Muhammad Bilal; Baleanu, Dumitru; Akg, Ali; Husnine, Syed Muhammad; Saeed, Syed TauseefConvective 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 temperature, 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. Additionally, 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.Article Shape Preserving Piecewise Knr Fractional Order Biquadratic C2 Spline(Wiley, 2021) Riaz, Muhammad Bilal; Jarad, Fahd; Jasim, Hayder Natiq; Enver, Aytekin; Kirmani, Syed Khawar NadeemIn a recent article, a piecewise cubic fractional spline function is developed which produces C-1 continuity to given data points. In the present paper, an interpolant continuity class C-2 is preserved which gives visually pleasing piecewise curves. he behavior of the resulting representations is analyzed intrinsically with respect to variation of the shape control parameters t and s. The data points are restricted to be strictly monotonic along real line.Article Citation - WoS: 19Citation - Scopus: 20New Optical Solitons of Fractional Nonlinear Schrodinger Equation With the Oscillating Nonlinear Coefficient: a Comparative Study(Elsevier, 2022) Riaz, Muhammad Bilal; Atangana, Abdon; Jahngeer, Adil; Jarad, Fahd; Awrejcewicz, JanIn this current exploration, some new optical soliton structures of fractional nonlinear Schrodinger equation with the oscillating nonlinear coefficient are constructed with three different definitions of fractional operators beta, Riemann-Liouville, and M-Truncated derivatives. These structures are computed with the help of the new auxiliary equation method. This method gives the new analytical solutions of the considered model. The analysis is done by considering the different definitions of the derivatives like Beta, Riemann-Liouville (RL), and M-Truncated derivatives. The considered equation is converted to an ordinary differential equation (ODE) by the use of this complex transformation. The graphical explanation of some obtained results is also elaborated in detail. This work is new and does not exist in literature.Article Citation - WoS: 7Citation - Scopus: 9An Exact and Comparative Analysis of Mhd Free Convection Flow of Water-Based Nanoparticles Via Cf Derivative(Hindawi Ltd, 2022) Aziz-Ur-Rehman, Aziz-Ur-; Riaz, Muhammad Bilal; Saeed, Syed Tauseef; Jarad, Fahd; Jasim, Hayder Natiq; Enver, AytekinConvective flow is a self-sustained flow with the effect of the temperature gradient. The density is nonuniform due to the variation in temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process, for instance, condensation, evaporation, and chemical process. Combination of water as base fluid and three types of nanoparticles named as copper, titanium dioxide, and aluminum oxide is taken into account. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD natural convection flow of water-based nano-particles in the presence of ramped conditions with Caputo-Fabrizio fractional time derivative. The exact fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform. The classical calculus is 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 the memory effect. But, in the fractional calculus (FC), the rate of change is affected by all points of the considered interval to incorporate the previous history/memory effects of any system. Due to this reason, we applied the modern definition of fractional derivative. Here, the order of the fractional derivatives will be treated as an index of memory. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). Our results suggest that the incremental value of the M is observed for a decrease in the velocity field, which reflects to control resistive force.Article Citation - WoS: 11Fractional Modeling of Viscous Fluid Over a Moveable Inclined Plate Subject To Exponential Heating With Singular and Non-Singular Kernels(Mdpi, 2022) Riaz, Muhammad Bilal; Rehman, Wajeeha; Awrejcewicz, Jan; Baleanu, Dumitru; Rehman, Aziz UrIn 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.Article Citation - WoS: 9Citation - Scopus: 9Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative(Asme, 2022) Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; Riaz, Muhammad BilalThis 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., beta = 0.1, the magnitude of truncated Mfractional derivative is greater whereas for increasing fractional orders, i.e., beta = 0.7 and beta = 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.Article Citation - WoS: 33Citation - Scopus: 33Construction of Traveling Waves Patterns of (1(Elsevier, 2020) Munawar, Maham; Riaz, Muhammad Bilal; Baleanu, Dumitru; Jhangeer, AdilIn 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 (G'/G2)-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.Article Citation - WoS: 4Citation - Scopus: 4Theoretical Study of Mhd Maxwell Fluid With Combined Effect of Heat and Mass Transfer Via Local and Nonlocal Time Derivatives(World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Asgir, Maryam; Riaz, Muhammad Bilal; Jarad, FahdThis study highlights the combined effect of heat and mass transfer on MHD Maxwell fluid under time-dependent generalized boundary conditions for velocity, temperature, and concentration. The classical calculus due to the fact that it is 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 the memory effect. But in the fractional calculus (FC), the rate of change is affected by all points of the considered interval, so it can incorporate the previous history/memory effects of any system. Due to this reason, we applied the modern definition of fractional derivatives (local and nonlocals kernels). Here, the order of fractional derivative will be treated as an index of memory. The exact and semi-analytical solutions are obtained using the integral transform and inversion algorithm. Several important properties of different parameters are analyzed by graphs. Interesting results are revealed by this investigation due to their vast applications in engineering and applied sciences.Article Citation - WoS: 37Citation - Scopus: 39A Mathematical Study of Natural Convection Flow Through a Channel With Non-Singular Kernels: an Application To Transport Phenomena(Elsevier, 2020) Riaz, Muhammad Bilal; Baleanu, Dumitru; Abro, Kashif Ali; Saeed, Syed TauseefIn 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 oABCTHORN and Caputo-Fabrizio oCFTHORN 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 alpha, D-f, G(m); G(r); S-c and P-r 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. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).Article Citation - WoS: 5Citation - Scopus: 7A 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(Sciendo, 2024) Jarad, Fahd; Riaz, Muhammad Bilal; Rehman, Aziz UrThe 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 u(0). 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 alpha, beta, P-r, Q, Gr, M, N-r 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.Article Citation - WoS: 1Citation - Scopus: 1Heat Transfer of Mhd Oldroyd-B Fluid With Ramped Wall Velocity and Temperature in View of Local and Nonlocal Differential Operators(World Scientific Publ Co Pte Ltd, 2022) Riaz, Muhammad Bilal; Jarad, Fahd; Asgir, MaryamThe 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.

