Yazar "Asjad, Muhammad Imran" seçeneğine göre listele

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    An analysis of a mathematical fractional model of hybrid viscous nanofluids and its application in heat and mass transfer
    (Elsevier, 2021) Ali, Rizwan; Asjad, Muhammad Imran; Akgul, Ali
    The present investigation deals with the application of novel way of modeling of heat and mass transfer flow of hybrid nanofluid (Aluminum and Copper) for different base fluid water and engine oil. The governing equations for energy and momentum equations are developed with Caputo fractional power law derivative through constitutive relations. The flow of nanofluids confined between the two parallel plates with distance d apart. This model can be solved by means of the Laplace transform technique. Statically analysis for Nusselt number and Sherwood number is also discussed. To see the impact of fractional parameters alpha, beta and gamma on the temperature, concentration and fluid velocity, we have plotted some graphs through MathCad software and presented in the graphical section. As a result, for small value of time, we found that temperature, concentration and velocity are minimum near the plate and for large time they are maximum away from the plate for different fractional parameters alpha, beta and gamma. That is, solutions show dual behavior and can be controlled by variation values of fractional parameters alpha, beta and gamma and decay for larger values of alpha and beta, respectively. Further, we concluded that water base hybrid nanofluids have higher temperature and velocity than engine oil based hybrid nanofluids. Also, we compared the present results with the recently published results and in limiting case they are in good agreement. (C) 2020 Elsevier B.V. All rights reserved.
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    Analysis of MHD viscous fluid flow through porous medium with novel power law fractional differential operator
    (Iop Publishing Ltd, 2020) Asjad, Muhammad Imran; Danish Ikram, Muhammadish; Akgul, Ali
    The present study deals with the unsteady and incompressible viscous fluid flow with constant proportional Caputo type fractional derivative (hybrid fractional operator). We find analytical solutions of a well-known problem in fluid dynamics known as Stokes' first problem. MHD and porosity are also considered as an additional effects. Using dimensional analysis, governing equations of motion converted into non-dimensional form and then extended with novel fractional operator of singular kernel and series solutions are obtained by Laplace transform method. As a result, we compared present result with all the existing fractional operators and found that momentum boundary layer thickness can be control by changing the value of fractional parameter. Moreover, it is also observed that constant proportional Caputo type operator is well suited in exhibiting the decay of velocity of the fluid than all the existing fractional operators with power law (C), exponential law (CF) and Mittage-Leffler law (ABC).
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    Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate
    (Amer Inst Mathematical Sciences-Aims, 2021) Ahmad, Mushtaq; Asjad, Muhammad Imran; Akgul, Ali; Baleanu, Dumitru
    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.
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    Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm
    (Elsevier B.V., 2021) Jhangeer, Adil; Faridi, Waqas Ali; Asjad, Muhammad Imran; Akgül, Ali
    This paper aims to study an improved perturbed Schrödinger equation (IPSE) with a kind of Kerr law non-linearity equation governing the propagation dynamics of soliton in optical fibers through the nano-optical fiber. The considered model predicts the influence of quantic non-linearity on the motion of ultrashort optical pulses. The integrability of the model is accompanied by the transformed rational function V-expansion method (for simplicity [Formula presented]). This proposed method is a significant mathematical tool to obtain the exact travelings wave solutions of non-linear complex partial differential equations (PDEs). A bunch of soliton solutions like dark, dark singular, plane wave solution, and periodic are retrieved along with suitable parametric values. The graphical analysis is also presented for the description of propagation of waves expressed by rational functions, hyperbolic functions, and trigonometric functions. © 2021 The Author(s)
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    Approximate Solutions for Higher Order Linear and Nonlinear Boundary Value Problems
    (Springer, 2021) Habib, Siddra; Azam, Muhammad Khurshid; Asjad, Muhammad Imran; Akgül, Ali
    Purpose: The specific objective of this study is to examine the higher order nonlinear BVPs (12th and 13th orders) which perform efficient role in the modeling of physical problems of science and engineering. Design/methodology/approach: An innovative modification of the homotopy perturbation (HP) technique by coupling it with the Laplace transform (LT) has been expended to solve linear and nonlinear higher order boundary-value problems (BVPs). A homotopy is constructed for the given problems (BVPs) by HP technique and solved it by temporal Laplace method. Then Laplace inversion procedure has been used for retrieving the initial dominion solution. Motivation: The motivation of this paper is to introduce an improved and fast converging technique to solve complex higher order nonlinear boundary value problems. Findings: The main finding in this paper is to analyze the higher order nonlinear ordinary differential equations with more accurate approximate solutions. The proposed HPLT solutions show that the present technique provides more accurate, efficient, fast convergence and comparatively small absolute errors for extensive finite range. The authors found no assumption for the constriction of this approach. The computer software Maple has been used to compute numerical results of BVPs. The results obtained from HPLT method are found in excellent agreement with the exact solutions. Research limitations/implications: This paper invokes these two main inspirations: firstly, Laplace transform is associated with homotopy perturbation method in a new manner, secondly, handling of boundary value problems with higher order. Practical implications: In this paper, the values of the approximate solution have excellent Promise with those of exact solutions. Social implications: This paper presents a valuable technique for handling the nonlinear higher order differential equations (ODEs) without involving any restrictions or hypothesis. Originality: The work in present article is original and advanced. Significantly, no such work has yet been published in the literature. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    Construction of optical solitons of Radhakrishnan-Kundu-Lakshmanan equation in birefringent fibers
    (Walter De Gruyter Gmbh, 2022) Ullah, Naeem; Asjad, Muhammad Imran; Rehman, Hamood Ur; Akgul, Ali
    In this article, we are attracted to discover the multiple-optical soiltons in birefringent fibers for Radhakrishnan-Kundu-Lakshmanan equation (RKLE) by applying the Sardar-subequation method (SSM) and the new extended hyperbolic function method (EHFM). We construct the solutions in the form of exponential, trigonometric, and hyperbolic functions solitons solutions like mixed complex solitons and multiple-optical solitons solutions. In addition, singular periodic wave solutions are constructed, and the restraint conditions for the presence of soliton solutions are also defined. Moreover, the physical interpretation of the obtained solutions is disclosed in forms of 3D and 2D plots for different suitable parameters. The attained results indicate that the implemented computational scheme is straight, proficient, and brief and can be applied in more complex phenomena with the associate of representative computations. We have obtained several sorts of new solutions.
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    Convective flow of a fractional second grade fluid containing different nanoparticles with Prabhakar fractional derivative subject to non-uniform velocity at the boundary
    (Wiley, 2023) Basit, Abdul; Asjad, Muhammad Imran; Akgul, Ali
    This article disputes the study of convective flow for improved nanofluid along with an erect heated plate via Prabhakar-like energy transport. The governing equations for this mathematical model are obtained by Prabhakar fractional derivative. To attain the generalized results for dimensionless velocity profile and temperature profile, a scheme of Laplace transform is applied. By applying the conditions of nanofluid flow, we develop the constantly accelerated, variables accelerated, and non-uniform accelerated solution of the model. Prabhakar fractional derivative for improved nanofluid based on generalized Fourier's thermal flux is determined for heat transfer. Different structures of graphs are performed for ordinary fractional parameters. As a result, it is found that temperature of Ag - H2O is higher than Cu - H2O and TiO2 - H2O nanoparticles and the reverse trend can be found for velocity. Furthermore, temperature and velocity can be enhanced by increasing the values of fractional parameters.
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    Dynamical analysis of solitons solutions of a nonlinear model with anti-cubic nonlinearity and Sardar-subequaion method
    (Inderscience Enterprises Ltd, 2024) Asjad, Muhammad Imran; Ullah, Naeem; Akgul, Ali
    In this study, our aim is to construct optical solitons for magneto-optic waveguides with anti-cubic nonlinearity. We would like to obtain the solutions in the form of hyperbolic and trigonometric functions solutions. We applied the Sardar-subequation method. The obtained results show that this technique is very active and efficient. The obtained solutions interpreted the wide-ranging diversity of solitons solutions. All obtained solutions are novel and unique from the stated results in literature. The acquired results are demonstrated by 3D and 2D plots to understand the real phenomena for such type of nonlinear models.
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    Effect of Slip on Generalized Viscous Nanofluid with Thermal Flux with Effective Fractional Derivative
    (Natural Sciences Publishing, 2022) Majeed, Usman; Asjad, Muhammad Imran; Qadir, Muhammad Irfan; Akgül, Ali
    In this article, the laminar boundary layer flow of a non-compressible viscous fluid with carbon nanotubes over an infinite vertical plate is taken into account. Our goal is to study the effects of slip boundary condition on the generalized viscous nanofluid over an infinite vertically positioned plate. The unsteady fractional Prabhakar derivative is used to introduce the correlated fractional system of the governing equations. We find the analytical expression of velocity of the fluid using the Laplace transform method. The results obtained in case of no slip effect are compared with the classical results. The impacts of fractional and physical factors are depicted graphically © 2022 NSP Natural Sciences Publishing Cor.
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    Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates
    (Elsevier, 2021) Ikram, Muhammad Danish; Asjad, Muhammad Imran; Akgul, Ali; Baleanu, Dumitru
    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/).
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    Exact solutions of convective-diffusive Cahn-Hilliard equation using extended direct algebraic method
    (Wiley, 2023) Rehman, Hamood Ur; Ullah, Naeem; Asjad, Muhammad Imran; Akgul, Ali
    In this paper, we apply the extended direct algebraic method to examine the soliton solutions as well as hyperbolic and trigonometric functions solutions of convective-diffusive Cahn-Hilliard equation describing the dynamic of separation phase for ternary iron alloys of (Fe - Cr - Mo) and (Fe - X - Cu). The outcomes reveal that our technique is very dynamic and straightforward. It is observed that the obtained exact solutions of this model are new in the literature. Moreover, various 2D and 3D graphs of the obtained solutions are presented to examine the physical understanding of the obtained results.
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    Generalized Thermal Flux Flow for Jeffrey Fluid with Fourier Law over an Infinite PlateY
    (Hindawi Ltd, 2021) Asjad, Muhammad Imran; Basit, Abdul; Akgul, Ali; Muhammad, Taseer
    The unsteady flow of Jeffrey fluid along with a vertical plate is studied in this paper. The equations of momentum, energy, and generalized Fourier's law of thermal flux are transformed to non-dimensional form for the proper dimensionless parameters. The Prabhakar fractional operator is applied to acquire the fractional model using the constitutive equations. To obtain the generalized results for velocity and temperature distribution, Laplace transform is performed. The influences of fractional parameters alpha,beta,gamma, thermal Grashof number Gr, and non-dimensional Prandtl number Pr upon velocity and temperature distribution are presented graphically. The results are improved in the form of decay of energy and momentum equations, respectively. The new fractional parameter contains the Mittag-Leffler kernel with three fractional parameters which are responsible for better memory of the fluid properties rather than the exponential kernel appearing in the Caputo-Fabrizio fractional operator. The Prabhakar fractional operator has advantage over Caputo-Fabrizio in the real data fitting where needed.
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    Heat transfer analysis of magnetohydrodynamic Casson fluid through a porous medium with constant proportional Caputo derivative
    (Wiley, 2021) Aleem, Maryam; Asjad, Muhammad Imran; Akgul, Ali
    This article aims to investigate free convection of a Casson fluid past a vertical plate embedded in porous medium with invariant wall temperature. It is assumed that the fluid can conduct electricity and it is flowing across a porous medium. The partial differential equations governing the model are made dimensionless by using dimensionless parameters. The Laplace transform method is applied to get analytical results. Furthermore, the hybrid fractional model is developed and the exact solutions for momentum and energy equations are acquired. The obtained results are compared with classical ones and the effect of hybrid fractional parameters are analyzed graphically by using MathCad software. Skin friction and heat transfer rate Nu is analyzed for small and large times and for hybrid fractional parameter beta. We also have seen the increasing velocity profiles for buoyancy parameter Gr, whereas temperature of the fluid decreases for Pr Pr. The rate of heat transfer (Nu) and skin friction (C-f) can be minimized by increasing the values of beta. Furthermore, the constant proportional Caputo derivative model exhibits more decay in velocity in comparison with classical model given in Khalid et al. Therefore, the constant proportional Caputo differential model demonstrates better memory function than the classical one. Moreover, the obtained results are identical to already published results of Khalid et al. and Imran et al.
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    Novel solitonic structure, Hamiltonian dynamics and lie symmetry algebra of biofilm
    (Elsevier B.V., 2024) Asghar, Umair; Asjad, Muhammad Imran; Faridi, Waqas Ali; Akgül, Ali
    In this study, the Lie point symmetries and optimal system have been established. We discuss the biofilm model's soliton solutions. To examine a nonlinear dynamical biofilm system, which is simply a bistable Allen–Cahn equation with quartic potential, to determine solitary wave profiles using the considered equation, a new auxiliary equation technique is used. A suitable variable transformation is used to convert the governing equation into a nonlinear ordinary differential equation. The unified approach is utilized to evaluate periodic solutions, solitary and soliton solutions as well as several newly discovered exact solitary wave solutions, it can be accomplished via Mathematica (https://www.wolfram.com/mathematica/online/). The new auxiliary equation approach is an efficient method for creating unique wave profiles based on a variety of soliton families. Also, the results are graphically visualized, by using the appropriate parametric settings. The outcomes are shown graphically in two dimensions, three dimensions, and contour form. The Hamiltonian conditions are satisfied by the planer dynamical framework of equations to ensure as the system that was generated is a conservative Hamiltonian dynamical system which includes all traveling wave structures. A sensitivity evaluation is used to explore the governing model's thoroughly dynamical properties. It is demonstrated that the model becomes more dependent on the beginning conditions than the variables. The strategy could be used to look for exact solutions to various nonlinear evolution equations. We believe that this study will have important applications in different areas of science. © 2024 The Author(s)
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    Novel waves structures for two nonlinear partial differential equations arising in the nonlinear optics via Sardar-subequation method
    (Elsevier, 2023) Ullah, Naeem; Asjad, Muhammad Imran; Hussanan, Abid; Akgul, Ali; Alharbi, Wedad R.; Algarni, H.; Yahia, I. S.
    In this paper, our aim is to construct the novel wave structures for two non-linear evo-lution equations which are rising in non-linear optics, mathematical biological models, fluid dynam-ics, waves theory, mechanics, quantum mechanics, and many more. We employed an efficient analytical technique namely, the Sardar-subequation method to build the wave solutions for the modified Benjamin-Bona-Mahony equation and the Coupled Klein-Gordon equations. We have built the numerous type of soliton wave structures of modified Benjamin-Bona-Mahony equation and the Coupled Klein-Gordon equations via the Sardar-subequation method. Acquired results reveal the dynamics behavior of waves structures including the bright, singular, dark, and periodic singular solitons solutions. To illustrate the behavior of these solutions some selected solutions are sketched in two-, and three-dimensional graphs. On the basis of these results, our technique is suit-able, up-to-date, and powerful. The obtained solutions are very efficacious and influential in non-linear optics, mathematical biology, mechanics, fluid mechanics, plasma physics, and many more. This study will assist to predict some new hypothesis and theories in the field of mathematical physics. (c) 2023 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/).
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    Numerical solutions of fractional Oldroyd-B hybrid nanofluid through a porous medium for a vertical surface
    (Taylor & Francis Ltd, 2022) Asjad, Muhammad Imran; Usman, Muhammad; Kaleem, Muhammad Mudassar; Akgul, Ali
    In this article , a mathematical model is developed inview of Caputo fractional derivative for Oldroyd-B hybrid nanofluid via a porous medium over a vertical surface. Nano-sized particles of Copper (Cu) and Titanium oxide (TiO2) are used to prepare a hybrid nanofluid taking water as a base fluid. The nonlinear governing equations of the problem are transformed into a dimensionless form using a dimensional analysis. A finite difference scheme is developed and applied successfully to get the numerical solutions of a deliberated problem. The influence of different physical parameters on the fluid velocity profile and temperature profile is analyzed briefly. The fractional parameter plays the role of controlling agent of thermal and momentum boundary layers. The fluid temperature boosted for ascending values of Eckert number Ec and similar behavior of temperature profile is observed for volume fraction parameter of nanoparticles phi. It can also be noticed that the extended finite difference scheme is an efficient tool and gives accurate results of the considered problem. It can be extended for more numerous types of heat transfer problems arising in physical science with complex geometries.
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    On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations
    (Mdpi, 2021) Asjad, Muhammad Imran; Ur Rehman, Hamood; Ishfaq, Zunaira; Awrejcewicz, Jan; Akgul, Ali; Riaz, Muhammad Bilal
    Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV-Caudery-Dodd-Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.
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    Power law memory of natural convection flow of hybrid nanofluids with constant proportional Caputo fractional derivative due to pressure gradient
    (Indian Acad Sciences, 2020) Ali, Rizwan; Akgul, Ali; Asjad, Muhammad Imran
    In this work, influence of hybrid nanofluids on heat transfer flow of a viscous fluid due to pressure gradient is discussed with innovative constant proportional Caputo fractional derivative. For this purpose, we consider an infinite vertical wall which is exponentially moving in the x-direction with variable temperature. Nanosized particles of Cu and Al2O3 are suspended in water, the base fluid. The governing equations of the problem are converted into dimensionless form. Further, we develop the constant proportional Caputo fractional model with a new operator with power law kernel which can be used to study the fluid behaviour for different values of fractional parameter at the present time. We applied the Laplace transform method to obtain the solutions and to see the impact of hybrid nanofluids and fractional parameter alpha respectively. We compared the present results with the recently published work (Nehad et al, Adv. Mech. Eng.11(7): 1 (2019)) with Caputo fractional derivative. As a result, we have found that the present solutions are best to describe the memory concept of temperature and velocity. For small values of fractional parameter, temperature and velocity have maximum values and for larger values of fractional parameter, temperature and velocity have minimum values. Further, rate of heat transfer and skin friction are also computed in tabular forms and it is found that Nusselt number with CPC is much less than that is computed with Caputo fractional derivative for greater values of fractional parameter alpha.
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    Soliton solutions of space-time fractional Zoomeron differential equation
    (Inderscience Enterprises Ltd, 2023) Rehman, Hamood Ur; Asjad, Muhammad Imran; Iqbal, Ifrah; Akgul, Ali
    In the present work, Sardar subequation method (SSM) is exerted for seeking exact solutions of (2 + 1)-dimensional space-time fractional Zoomeron equation (FZE) in terms of conformable derivative (CD). The conformable derivative has much more capability than Riemann-Liouville and caputo derivative in solving the nonlinear fractional differential equation. The proposed method is extremely simple and very effective for finding exact solutions and then extracting solitons for the model. Bright, dark, singular, periodic singular and bright-dark hybrid soliton solutions are retrieved. Appropriate constraints are chosen for the obtained solitons to guarantee their existence. Moreover, from some obtained solutions, we draw its two-dimensional, contour and three-dimensional graphs by taking suitable values of parameters and then compare these graphs by changing the values of conformable derivative.
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    Study of Results of Katugampola Fractional Derivative and Chebyshev Inequailities
    (Springer, 2022) Nazeer, Nazakat; Asjad, Muhammad Imran; Azam, Muhammad Khursheed; Akgül, Ali
    In this work, we use generalized form of Caputo-type fractional derivative and Riemann–Liouville fractional Integral which is known as Katugampola fractional derivative. This work deals with some results having applications of Katugampola fractional derivative. We discuss commutative and inverse property of Katugampola fractional derivative. We have also introduced Chebyshev inequalities and some other integrals inequalities applying the Katugampola fractional derivative. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.