Browsing by Author "Abbas, Muhammad"

Now showing 1 - 15 of 15

Citation Count: Amin, Muhammad...et al. (2019) "A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations", Advances in Difference Equations, Vol. 2019, No. 1.
A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations
(Springer, 2019) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Ismail, Ahmad Izani Md.; Baleanu, Dumitru; 56389
The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h4+ Δ t2) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature. © 2019, The Author(s).
Citation Count: Arshad, Muhammad Sarmad...et al. (2020). "A Novel 2-Stage Fractional Runge-Kutta Method for a Time-Fractional Logistic Growth Model", Discrete Dynamics in Nature and Society, Vol. 2020.
A Novel 2-Stage Fractional Runge-Kutta Method for a Time-Fractional Logistic Growth Model
(2020) Arshad, Muhammad Sarmad; Baleanu, Dumitru; Riaz, Muhammad Bilal; Abbas, Muhammad; 56389
In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge-Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge-Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.
Citation Count: Khalid, Nauman...et al. (2019). "A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms", Advances in Difference Equations, Vol. 2019, No. 1.
A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms
(Springer Open, 2019) Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.
Citation Count: Akram, Tayyaba...et al. (2020). "A Numerical Approach of a Time Fractional Reaction-Diffusion Model with a Non-Singular Kernel", Symmetry-Basel, Vol. 12, No. 10.
A Numerical Approach of a Time Fractional Reaction-Diffusion Model with a Non-Singular Kernel
(2020) Akram, Tayyaba; Abbas, Muhammad; Ali, Ajmal; Iqbal, Azhar; Baleanu, Dumitru; 56389
The time-fractional reaction-diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo-Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions.
Citation Count: Khalid, Nauman...et al. (2020). "A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions", Advances in Difference Equations, Vol. 2020, No. 1.
A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions
(2020) Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen-Cahn equation (ACE). We discretize the time fractional derivative of order alpha is an element of (0,1] by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order O(h2+Delta t2-alpha) and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature.
Citation Count: Huntul, M. J.; Abbas, Muhammad; Baleanu, Dumitru (2021). "An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation", Advances in Difference Equations, Vol. 2021, No. 1.
An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation
(2021) Huntul, M. J.; Abbas, Muhammad; Baleanu, Dumitru; 56389
In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank-Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.
Citation Count: Sadaf, Maasoomah...et.al. (2023). "Dynamics Of Unsteady Fluid-Flow Caused By A Sinusoidally Varying Pressure Gradient Through A Capillary Tube With Caputo-Fabrizio Derivative", Thermal Science, Vol.27, No.SI1, pp.S49-S56.
Dynamics Of Unsteady Fluid-Flow Caused By A Sinusoidally Varying Pressure Gradient Through A Capillary Tube With Caputo-Fabrizio Derivative
(2023) Sadaf, Maasoomah; Perveen, Zahida; Zainab, Iqra; Akram, Ghazala; Abbas, Muhammad; Baleanu, Dumitru; 56389
This paper presents a study of the unsteady flow of second grade fluid through a capillary tube, caused by sinusoidally varying pressure gradient, with fractional derivative model. The fractional derivative is taken in Caputo-Fabrizio sense. The analytical solution for the velocity profile has been obtained for non-homogenous boundary conditions by employing the Laplace transform and the finite Hankel transform. The influence of order of Caputo-Fabrizio time-fractional derivative and time parameter on fluid motion is discussed graphically.
Citation Count: Akram, Tayyaba...et al. (2019). "Extended cubic B-splines in the numerical solution of time fractional telegraph equation", Advances in Difference Equations, Vol. 2019, No. 1.
Extended cubic B-splines in the numerical solution of time fractional telegraph equation
(Springer Open, 2019) Akram, Tayyaba; Abbas, Muhammad; İsmail, Ahmad İzani; Ali, Norhashidah Hj M.; Baleanu, Dumitru; 56389
A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.
Citation Count: Rashid, Umair...et al. (2020). "Marangoni boundary layer flow and heat transfer of graphene-water nanofluid with particle shape effects", Processes, Vol. 8, No. 9.
Marangoni boundary layer flow and heat transfer of graphene-water nanofluid with particle shape effects
(2020) Rashid, Umair; Baleanu, Dumitru; Liang, Haiyi; Abbas, Muhammad; Iqbal, Azhar; ul Rahman, Jamshid; 56389
Graphene nanofluids have attracted the attention of many researchers because of a variety of remarkable properties such as extraordinary electronic transport properties, high thermal conductivity, and large specific surface areas. This paper investigates the shape effects of nanoparticles on the Marangoni boundary layer of graphene-water nanofluid flow and heat transfer over a porous medium under the influences of the suction parameter. The graphene-water nanofluid flow was contained with various shapes of nanoparticles, namely sphere, column, platelet, and lamina. The problem is modeled in form of partial differential equations (PDES) with boundary conditions. The governing transport equations are converted into dimensionless form with the help of some suitable nondimensional variables. The solution of the problem was found numerically using the NDSolve technique of Mathematica 10.3 software. In addition, the numerical solutions were also compared with analytical results. The homotopy analysis method (HAM) is used to calculate the analytical results. The results show that lamina-shaped nanoparticles have better performance on temperature distribution while sphere-shaped nanoparticles are more efficient for heat transfer than other shapes of nanoparticles. © 2020 by the authors.
Citation Count: Amin, Muhammad...et al. (2019). "Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations", Advances in Difference Equations.
Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations
(Springer Open, 2019) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.
Citation Count: Akram, Tayyaba...et al. (2020). "Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation", Symmetry-Basel, Vol. 12, No. 7.
Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation
(2020) Akram, Tayyaba; Abbas, Muhammad; Iqbal, Azhar; Baleanu, Dumitru; Asad, Jihad H.; 56389
The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor's series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.
Citation Count: Amin, Muhammad...et al. (2020). "Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions", Frontiers in Physics, Vol. 8.
Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions
(2020) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein–Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order α ∈ (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme is O(h2 + Δt2−α) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.
Citation Count: Amin, Muhammad...et al. (2021). "Redefined extended cubic B-spline functions for numerical solution of time-fractional telegraph equation", CMES - Computer Modeling in Engineering and Sciences, Vol. 127, No. 1, pp. 361-384.
Redefined extended cubic B-spline functions for numerical solution of time-fractional telegraph equation
(2021) Amin, Muhammad; Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; 56389
This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.
Citation Count: Akram, Ghazala;...et.al. (2023). "Solitary wave solutions to Gardner equation using improved (Ω(sic)/2 ) tan 2 -expansion method", AIMS Mathematics, Vol.8, No.2, pp.4390-4406.
Solitary wave solutions to Gardner equation using improved (Ω(sic)/2 ) tan 2 -expansion method
(2023) Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru; 56389
In this study, the improved tan(Omega(sic)/2 )-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.
Citation Count: Akram, Ghazala...et al (2023). "Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method", AIMS Mathematics, Vol. 8, No. 2, pp. 4390-4406.
Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method
(2023) Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru; 56389
In this study, the improved tan(Ω(Υ)/2-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.