Browsing by Author "Asjad, Muhammad Imran"

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Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "A Nonsingular Fractional Derivative Approach for Heat and Mass Transfer Flow with Hybrid Nanoparticles", Journal of Mathematics, Vol.2022.
A Nonsingular Fractional Derivative Approach for Heat and Mass Transfer Flow with Hybrid Nanoparticles
(2022) Asjad, Muhammad Imran; Naz, Rabia; Ikram, Muhammad Danish; Iqbal, Azhar; Jarad, Fahd; 234808
This paper deals with the study of MHD Brinkman type fluid flow containing hybrid titanium (TiO2) and silver (Ag) nanoparticles with nonlocal noninteger type Atangana-Baleanu (ABC) fractional differential operator. The problem is designed for the convective flow restrained in a microchannel. With the Mittag-Leffler kernel, the conventional governing equations are converted into dimensionless form and then generalised with noninteger order fractional operators. The solutions for temperature and velocity fields obtained via Laplace transform method and expressed in the series form. The effect of related parameters is dignified graphically with the help of Mathcad and presented in the graphical section. Finally, the results show that the AB fractional operator exhibited improved memory effect as compared to CF fractional operator. Furthermore, due to increasing the values volume fractional temperature can be enhanced and velocity decreases. In comparison between nanoparticles for different types of based fluid, velocity and temperature of water based (TiO2) and silver (Ag) is higher than other base fluids.
Citation Count: Ahmad, Mushtaq...at all (2021). "Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate", AIMS Mathematics, Vol. 6, No. 3, pp. 2344-2358.
Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate
(2021) Ahmad, Mushtaq; Asjad, Muhammad Imran; Akgül, Ali; Baleanu, Dumitru; 56389
This research article is design to elaborate the rule and significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluids namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermophysical properties of nanoparticles. Also the geometric and thermal conditions are imposed in flow domain. In the governing equations, the partial derivative with respect to time replaced by new hybrid fractional derivative and then solved analytically for temperature and velocity field with the help of Laplace transformed. The obtained solutions for temperature and velocity are presented geometrically by Mathcad software to see the effectiveness of potent parameters. The temperature and velocity present a significant increasing trend for increasing volume fraction parameter. The obtained results for temperature as well as velocity are also compared with the existing literature and it is concluded that field variables with new hybrid fractional derivative, show more decaying trend as compare to the results with Caputo and Caputo-Fabrizio fractional derivatives.
Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "Bioconvection Flow of MHD Viscous Nanofluid in the Presence of Chemical Reaction and Activation Energy", Mathematical Problems in Engineering, Vol.2022.
Bioconvection Flow of MHD Viscous Nanofluid in the Presence of Chemical Reaction and Activation Energy
(2022) Asjad, Muhammad Imran; Zahid, Muhammad; Jarad, Fahd; Alsharif, Abdullah M.; 234808
Enhancement of heat transfer due to stretching sheets can be appropriately controlled by the movement of the nanofluids. The concentration and settling of the nanoparticles in the viscous MHD fluid and bioconvection are addressed. In this scenario, the fluid flow occurring in the presence of a normal and uniform magnetic field, thermal radiation, and chemical reaction is taken into account. For the two-dimensional flow with heat and mass transfer, five dependent variables and three independent variables constitute the system of partial differential equations. For this purpose, similarity functions are involved to convert these equations to corresponding ODEs. Then, the Runge-Kutta method with shooting technique is used to evaluate the required findings with the utilization of MATLAB script. The fluid velocity becomes slow against the strength of the magnetic parameter. The temperature rises with the parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruences.
Citation Count: Ishtiaq, Umar...et.al. (2023). "Common fixed point, Baire’s and Cantor’s theorems in neutrosophic 2-metric spaces", AIMS Mathematics, Vol.8, No.2, pp.2532-2555.
Common fixed point, Baire’s and Cantor’s theorems in neutrosophic 2-metric spaces
(2023) Ishtiaq, Umar; Ahmad, Khaleel; Asjad, Muhammad Imran; Ali, Farhan; Jarad, Fahd; 234808
These fundamental Theorems of classical analysis, namely Baire’s Theorem and Cantor’s Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire’s Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces.
Citation Count: Shafique, Ahmad;...et.al. (2022). "Effect of Diffusion-Thermo on MHD Flow of a Jeffrey Fluid Past an Exponentially Accelerated Vertical Plate with Chemical Reaction and Heat Generation", Mathematical Problems in Engineering, Vol.2022, pp.1-13.
Effect of Diffusion-Thermo on MHD Flow of a Jeffrey Fluid Past an Exponentially Accelerated Vertical Plate with Chemical Reaction and Heat Generation
(2022) Shafique, Ahmad; Nisa, Zaib Un; Asjad, Muhammad Imran; Nazar, Mudassar; Jarad, Fahd; 234808
In many flow phenomenons of fluid with medium molecular weight, the energy flux is effected due to the inhomogeneity of concentration of mass. This contribution of the concentration to the energy flux is considered as diffusion-thermo effect or Dufour effect. In this research article the diffusion-thermo effect is addressed for the magnetohydrodynamics (MHD) flow of Jeffrey's fractional fluid past an exponentially accelerated vertical plate with generalized thermal and mass transports through a porous medium. For the generalization of the thermal and mass fluxes the constant proportional Caputo (CPC) fractional derivative is utilized. The governing of this generalized flow are reduced to non-dimensional forms and then solved semi analytically by Laplace transform. In additions the physical aspects of flow and material parameters especially the effect of Du and fractional parameters are discussed by sketching the graphs. From the graphical illustration, it is concluded that in the presence of Dufour effect flow speeds up. Moreover, a comparison between fractionalized and ordinary velocity fields is also drawn and it is also observed that fractional model with constant proportional derivative is of the more decaying nature as compare to the model contracted with classical Caputo and Caputo fractional derivatives.
Citation Count: Ikram, Muhammad Danish...et al. (2021). "Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates", Alexandria Engineering Journal, Vol. 60, No. 4, pp. 3593-3604.
Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates
(2021) Ikram, Muhammad Danish; Asjad, Muhammad Imran; Akgül, Ali; Baleanu, Dumitru; 56389
In this paper, it has been discussed the fractional model of Brinkman type fluid (BTF) holding hybrid nanoparticles. Titanium dioxide (TiO2) and silver (Ag) nanoparticles were liquefied in water (H2O) (base fluid) to make a hybrid nanofluid. The magnetohydrodynamic (MHD) free convection flow of the nanofluid (Ag - TiO2 - H2O)was measured in a bounded microchannel. The BTF model was generalized using constant proportional Caputo fractional operator (CPC) with effective thermophysical properties. By introducing dimensionless variables, the governing equations of the model were solved by Laplace transform method. The testified outcomes are stated as M-function. The impact of associated parameters were measured graphically using Mathcad and offered a comparison with the existing results from the literature. The effect of related parameters was physically discussed. It was concluded that constant proportional Caputo fractional operator (CPC) showed better memory effect than Caputo-Fabrizio fractional operator (CF) (Saqib et al., 2020). (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation Count: Chu, Yu-Ming;...et.al. (2021). "Fractional Model Of Second Grade Fluid Induced By Generalized Thermal And Molecular Fluxes With Constant Proportional Caputo", Thermal Science, Vol.25, No.2, pp.207-212.
Fractional Model Of Second Grade Fluid Induced By Generalized Thermal And Molecular Fluxes With Constant Proportional Caputo
(2021) Chu, Yu-Ming; Ahmad, Mushtaq; Asjad, Muhammad Imran; Baleanu, Dumitru; 56389
In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.
Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "Impact of activation energy and MHD on Williamson fluid flow in the presence of bioconvection", Alexandria Engineering Journal, Vol.61, No.11, pp.8715-8727.
Impact of activation energy and MHD on Williamson fluid flow in the presence of bioconvection
(2022) Asjad, Muhammad Imran; Zahid, Muhammad; Inc, Mustafa; Baleanu, Dumitru; Almohsen, Bandar; 56389
The main purpose of the current study is to invetigate the influence of Brownian motion and thermophoresis diffusion in non-Newtonian Williamson fluid flow through exponentially stretching sheet with the effects of thermal radiation and the bioconvection of microorganisms. For this purpose, similarity functions are involved to transmute partial differential equations to corresponding ordinary differential equations. Then Runge–Kutta method with shooting technique is hired to evaluate the desired findings with utilization of MATLAB script. The fluid velocity becomes slow against strength of magnetic parameter and it boosts with mixed convection. The temperature rises with parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruence's.
Citation Count: Lashin, Maha M. A.;...et.al. (2022). "Magnetic Field Effect on Heat and Momentum of Fractional Maxwell Nanofluid within a Channel by Power Law Kernel Using Finite Difference Method", Complexity, Vol.2022.
Magnetic Field Effect on Heat and Momentum of Fractional Maxwell Nanofluid within a Channel by Power Law Kernel Using Finite Difference Method
(2022) Lashin, Maha M. A.; Usman, Muhammad; Asjad, Muhammad Imran; Ali, Arfan; Jarad, Fahd; Muhammad, Taseer; 234808
The mathematical model of physical problems interprets physical phenomena closely. This research work is focused on numerical solution of a nonlinear mathematical model of fractional Maxwell nanofluid with the finite difference element method. Addition of nanoparticles in base fluids such as water, sodium alginate, kerosene oil, and engine oil is observed, and velocity profile and heat transfer energy profile of solutions are investigated. The finite difference method involving the discretization of time and distance parameters is applied for numerical results by using the Caputo time fractional operator. These results are plotted against different physical parameters under the effects of magnetic field. These results depicts that a slight decrease occurs for velocity for a high value of Reynolds number, while a small value of Re provides more dominant effects on velocity and temperature profile. It is observed that fractional parameters α and β show inverse behavior against uy,t and θy,t. An increase in volumetric fraction of nanoparticles in base fluids decreases the temperature profile of fractional Maxwell nanofluids. Using mathematical software of MAPLE, codes are developed and executed to obtain these results.
Citation Count: Faridi, Waqas Ali; Asjad, Muhammad Imran; Jarad, Fahd. (2022). "Non-linear soliton solutions of perturbed Chen-Lee-Liu model by Φ 6- model expansion approach", Optical and Quantum Electronics, Vol.54, No.10.
Non-linear soliton solutions of perturbed Chen-Lee-Liu model by Φ 6- model expansion approach
(2022) Faridi, Waqas Ali; Asjad, Muhammad Imran; Jarad, Fahd; 234808
This study deals with the perturbed Chen-Lee-Liu governing mode which portrays the propagating phenomena of the optical pulses in the discipline of optical fiber and plasma. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we use an analytical approach to find traveling wave solutions. One of the generalized techniques Φ 6- model expansion method is exerted to find new solitary wave profiles. It is an effective, and reliable technique that provides generalized solitonic wave profiles including numerous types of soliton families. As a result, solitonic wave patterns attain, like Jacobi elliptic function, periodic, dark, bright, singular, dark-bright, exponential, trigonometric, and rational solitonic structures, etc. The constraint corresponding to each obtained solution provides the guarantee of the existence of the solitary wave solutions. The graphical 2-D, 3-D, and contour visualization of the obtained results is presented to express the pulse propagation behaviors by assuming the appropriate values of the involved parameters. The Φ 6- model expansion method is simple which can be easily applied to other complex non-linear models and get solitary wave structures.
Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "Nonlinear wave train in an inhomogeneous medium with the fractional theory in a plane self-focusing", AIMS Mathematics, Vol.7, No.5, pp.8290-8313.
Nonlinear wave train in an inhomogeneous medium with the fractional theory in a plane self-focusing
(2022) Asjad, Muhammad Imran; Faridi, Waqas Ali; Jhangeer, Adil; Aleem, Maryam; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; 56389
The aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional β differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and β fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and β-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.
Citation Count: Ullah, Naeem;...et.al. (2022). "On soliton solutions of fractional-order nonlinear model appears in physical sciences", AIMS Mathematics, Vol.7, No.5, pp.7421-7440.
On soliton solutions of fractional-order nonlinear model appears in physical sciences
(2022) Ullah, Naeem; Asjad, Muhammad Imran; Awrejcewicz, Jan; Muhammad, Taseer; Baleanu, Dumitru; 56389
In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)- dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardarsubequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.
Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "Optical solitons for conformable space-time fractional non-linear model", Journal of Mathematics and Computer Science, Vol.27, No.1, pp.28-41.
Optical solitons for conformable space-time fractional non-linear model
(2022) Asjad, Muhammad Imran; Ullah, Naeem; Rehman, Hamood Ur; Baleanu, Dumitru; 56389
In search of the exact solutions of nonlinear partial differential equations in solitons form has become most popular to understand the internal features of physical phenomena. In this paper, we discovered various type of solitons solutions for the conformable space-time nonlinear Schrödinger equation (CSTNLSE) with Kerr law nonlinearity. To seek such solutions, we applied two proposed methods which are Sardar-subequation method and new extended hyperbolic function method. In this way several types of solitons obtained for example bright, dark, periodic singular, combined dark-bright, singular, and combined singular solitons. Some of the acquired solutions are interpreted graphically. These solutions are specific, novel, correct and may be beneficial for edifying precise nonlinear physical phenomena in nonlinear dynamical schemes. It is revealed that the proposed methods offer a straightforward and mathematical tool for solving nonlinear conformable space-time nonlinear Schrödinger equation. These results support in attaining nonlinear optical fibers in the future.
Citation Count: Arora, Geeta;...et.al. (2023). "Particle Swarm Optimization for Solving Sine-Gordan Equation", Computer Systems Science and Engineering, Vol.45, No.3, pp.2647-2658.
Particle Swarm Optimization for Solving Sine-Gordan Equation
(2023) Arora, Geeta; Chauhan, Pinkey; Asjad, Muhammad Imran; Joshi, Varun; Emadifar, Homan; Jarad, Fahd; 234808
The term 'optimization' refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm optimization technique to find a numerical solution for the Sine-Gordan equation, whose numerical solutions show the soliton form and has diverse applications. The implemented optimization technique is employed to determine the involved parameter in the basis functions, which was previously approximated as a random number in the work reported till now in the literature. The obtained results are comparable with the results obtained in the literature. The work is presented in the form of figures and tables and is found encouraging.
Citation Count: Asjad, Muhammad Imran;...et.al. (2021). "Prabhakar Fractional Derivative And Its Applications In The Transport Phenomena Containing Nanoparticles", Thermal Science, Vol.28, No.SI, pp.411-416.
Prabhakar Fractional Derivative And Its Applications In The Transport Phenomena Containing Nanoparticles
(2021) Asjad, Muhammad Imran; Zahid, Muhammad; Chu, Yu-Ming; Baleanu, Dumitru; 56389
In this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.
Citation Count: Asjad, Muhammad Imran...et.al. (2022). "Study of power law non-linearity in solitonic solutions using extended hyperbolic function method", AIMS Mathematics, Vol.7, No.10, pp.18603-18615.
Study of power law non-linearity in solitonic solutions using extended hyperbolic function method
(2022) Asjad, Muhammad Imran; Ullah, Naeem; Taskeen, Asma; Jarad, Fahd; 234808
This paper retrieves the optical solitons to the Biswas-Arshed equation (BAE), which is examined with the lack of self-phase modulation by applying the extended hyperbolic function (EHF) method. Novel constructed solutions have the shape of bright, singular, periodic singular, and dark solitons. The achieved solutions have key applications in engineering and physics. These solutions define the wave performance of the governing models. The outcomes show that our scheme is very active and reliable. The acquired results are illustrated by 3-D and 2-D graphs to understand the real phenomena for such sort of non-linear models.
Citation Count: Faridi, Waqas Ali; Asjad, Muhammad Imran; Jarad, F. (2022). "The fractional wave propagation, dynamical investigation, and sensitive visualization of the continuum isotropic bi-quadratic Heisenberg spin chain process", Results in Physics, Vol.43.
The fractional wave propagation, dynamical investigation, and sensitive visualization of the continuum isotropic bi-quadratic Heisenberg spin chain process
(2022) Faridi, Waqas Ali; Asjad, Muhammad Imran; Jarad, Fahd; 234808
This paper deals with the Lakshmanan-Porsezian-Daniel equation which delineates the continuum isotropic bi-quadratic Heisenberg spin chain phenomenon. A new auxiliary equation method is exerted on the considered equation to find solitary wave profiles. It is a simple and powerful approach for developing innovative wave profiles based on diverse soliton families such as trigonometric functions, rational, hyperbolic trigonometric function and exponential function etc. As a result, the solitonic wave patterns attain such as dark, bright, dark-bright, singular, rational, periodic-singular, exponential, and periodic solitons etc. The deep dynamical aspects of the governing model study by performing the chaos and sensitivity analysis. The planer dynamical system of equation develop and satisfy the Hamiltonian criteria to assure that, the developed system is Hamiltonian dynamical system and contains all traveling wave structures and the system is conservative. The graphical explanation of energy levels presents the significant insights and the existence of closed-form solutions to the model. The periodic, quasi-periodic, and quasi-periodic-chaotic profiles are present to see the deep dynamics of the continuum isotropic bi-quadratic Heisenberg spin chain system. The graphically visualization for sensitivity analysis of the governing equation portraits by taking some initial values to verify its dependence. It is shown that, the model is more sensitive regarding to initial conditions rather then parameters. The graphical two dimensional, three dimensional, and contour visualization of the obtained results are presented to express the pulse propagation behavior by assuming the appropriate values of the involved parameters. The impact of fractional parameter is displayed in the graphical sense. The fractional order controls the soliton behaviour which means that, the prediction and precautions can be constructed about the physical phenomenon of the continuum isotropic bi-quadratic Heisenberg spin chain. As a results, the fractional order exhibits the states of distortion in continuum bi-quadratic magnetic system with non-zero vector on which the form evaluates to zero. The graphical two dimensional, three dimensional, and contour visualization of the obtained results are presented to express the pulse propagation behavior by assuming the appropriate values of the involved parameters.
Citation Count: Li, Shuo;...et.al. (2023). "The impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical model", Chaos, Solitons and Fractals, Vol.173.
The impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical model
(2023) Bukhsh, Imam; Asjad, Muhammad Imran; Eldin, Sayed M.; El-Rahman, Magda Abd; Baleanu, Dumitru; Li, Shuo; 56389
Mathematical models are enormously valuable in recognition the characteristics of infectious afflictions. The present study describes and analyses a nonlinear Susceptible-Infected (S·I) type mathematical model for HIV/AIDS. To better comprehend the dynamics of disease diffusion, it is assumed that by giving AIDS patients timely Anti Retroviral Therapy (ART), their transition into HIV infected class is attainable. The ART treatment can reduce or manage the spread of disease among individuals that can extend their life for some more years. For the model, the basic reproduction number is formed which provides a base to study the stability of disease free and endemic equilibria. To understand the entire dynamical behavior of the model, standard finite difference (SFD) schemes such as Runge-Kutta of order four (RK-4) and forward Euler schemes and nonstandard finite difference (NSFD) scheme are implemented. The goal of constructing the NSFD scheme for differential equations is to ensure that it is dynamically reliable, while maintaining important dynamical properties like the positivity of the solutions and its convergence to equilibria of continuous model for all finite step sizes. However, the essential characteristics of the continuous model cannot be properly maintained by the Euler and RK-4 schemes, leading to the possibility of numerical solutions that are not entirely similar to those of the original model. For the NSFD scheme, the Routh-Hurwitz criterion is used to assess the local stability of disease-free and endemic equilibria. To explain the global stability of both the equilibria, Lyapunov functions are offered. To verify the theoretical findings and validate the dynamical aspects of the abovementioned schemes, numerical simulations are also provided. The outcomes offered in this study may be engaged as an effective tool for forecasting the progression of HIV/AIDS epidemic diseases.
Citation Count: Asjad, Muhammad Imran...et.al. (2022). "Unsteady Casson fluid flow over a vertical surface with fractional bioconvection", AIMS Mathematics, Vol.7, No.5, pp.8112-8126.
Unsteady Casson fluid flow over a vertical surface with fractional bioconvection
(2022) Asjad, Muhammad Imran; Butt, Muhammad Haris; Sadiq, Muhammad Armaghan; Ikram, Muhammad Danish; Jarad, Fahd; 234808
This paper deals with unsteady flow of fractional Casson fluid in the existence of bioconvection. The governing equations are modeled with fractional derivative which is transformed into dimensionless form by using dimensionless variables. The analytical solution is attained by applying Laplace transform technique. Some graphs are made for involved parameters. As a result, it is found that temperature, bioconvection are maximum away from the plate for large time and vice versa and showing dual behavior in their boundary layers respectively. Further recent literature is recovered from the present results and obtained good agreement.