Browsing by Author "Hashemi, Mir Sajjad"

Now showing 1 - 8 of 8

A geometric approach for solving the density-dependent diffusion Nagumo equation
(Springer International Publishing, 2016) Baleanu, Dumitru; Darvishi, Elham; Baleanu, Dumitru
In this paper, some solutions of the density-dependent diffusion Nagumo equation are obtained by using a new approach, the Lie symmetry group-preserving scheme (LSGPS). The effects of various model parameters on the solution are investigated graphically using LSGPS. Finally, a different reduction method of PDEs is applied to construct two new analytical solutions and a first integral of the Nagumo equation.
A new application of the Legendre reproducing kernel method
(2022) Jarad, Fahd; Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgül, Ali; Jarad, Fahd; 234808
n this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.
Exact Solutions, Lie Symmetry Analysis and Conservation Laws of the Time Fractional Diffusion-Absorption Equation
(2019) Baleanu, Dumitru; Balmeh, Zahra; Baleanu, Dumitru; 56389
New Method For Investigating the Density-Dependent Diffusion Nagumo Equation
(Vinca Inst Nuclear Sci, 2018) Baleanu, Dumitru; Hashemi, Mir Sajjad; İnç, Mustafa; Khan, Hasib; Baleanu, Dumitru; 56389
We apply reproducing kernel method to the density-dependent diffusion Nagumo equation. Powerful method has been applied by reproducing kernel functions. The approximations to the exact solution are obtained. In particular, series solutions are obtained. These solutions demonstrate the certainty of the method The results acquired in this work conceive many attracted behaviors that assure further work on the Nagumo equation.
New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space with Three Types of Local Derivatives
(2022) Jarad, Fahd; Hashemi, Mir Sajjad; Jarad, Fahd; 234808
The aim of this paper is to use the Nucci’s reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors’ knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.
On fractional KdV-Burgers and potential KdV equations: Existence and uniqueness results
(2019) Baleanu, Dumitru; İnç, Mustafa; Baleanu, Dumitru; 56389
Recently a new kind of derivatives, namely the conformable derivative is introduced which have not many drawbacks of other fractional derivatives. Two types of KdV equations with conformable derivative are investigated in this paper. Existence and uniqueness of two different equations of KdV class with conformable derivatives are investigated. It is also shown that the invariant subspace method can be extended to find the exact solutions of these equations.
Solving the Lane-Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme
(MDPI, 2017) Baleanu, Dumitru; Akgül, Ali; İnç, Mustafa; Mustafa, Idrees Sedeeq; Baleanu, Dumitru; 56389
We apply the reproducing kernel method and group preserving scheme for investigating the Lane-Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These approximations demonstrate the preciseness of the investigated techniques.
Solving the time-fractional diffusion equation using a lie group integrator
(Vinca Inst Nuclear Sci, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Parto-Haghighi, Mohammad; Darvishi, Elham
In this paper, we propose a numerical method to approximate the solutions of time fractional diffusion equation which is in the class of Lie group integrators. Our utilized method, namely fictitious time integration method transforms the unknown dependent variable to a new variable with one dimension more. Then the group preserving scheme is used to integrate the new fractional partial differential equations in the augmented space R3+1. Effectiveness and validity of method demonstrated using two examples.