Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 30Citation - Scopus: 33Dynamics of Fractional Order Delay Model of Coronavirus Disease(Amer inst Mathematical Sciences-aims, 2022) Zhang, Lei; Rahman, Mati Ur; Ahmad, Shabir; Riaz, Muhammad Bilal; Jarad, FahdThe majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.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: 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 Shape Preserving Piecewise Knr Fractional Order Biquadratic C<sup>2</Sup> 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: 27Citation - Scopus: 30Generalized 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 <mml:semantics>alpha</mml:semantics>, <mml:semantics>Pr</mml:semantics>, <mml:semantics>beta</mml:semantics>, <mml:semantics>Sc</mml:semantics>, <mml:semantics>Gr</mml:semantics>, <mml:semantics>gamma</mml:semantics>, and <mml:semantics>Gm</mml:semantics> 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: 25Citation - Scopus: 29Investigation 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: 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, Maryam; Zafar, Azhar AliThe 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.Article Citation - WoS: 36Citation - Scopus: 38Construction 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: 45Citation - Scopus: 50A Reduction Technique To Solve the Generalized Nonlinear Dispersive Mk(M,n) Equation With New Local Derivative(Elsevier, 2022) Jarad, Fahd; Hashemi, Mir Sajjad; Riaz, Muhammad Bilal; Xia, Fang-LiIn this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci's reduction technique. Combinations of the exponential, trigonometric, hyperbolic, and logarithmic functions constitute the exact solutions especially of the soliton and Kink-type soliton solutions. The influence of the derivative order alpha, for the obtained results, is graphically investigated. In some cases, exact solutions are achieved for arbitrary values of n and m, which can be interesting from the mathematical point of view. We provided 2-D and 3-D figures to illustrate the reported solutions. Computational results indicate that the reduction technique is superior to some other methods used in the literature to solve the same equations. To the best of the author's knowledge, this method is not applied for differential equations with the recently hyperbolic local derivative.Article Citation - WoS: 25Citation - Scopus: 25A 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.