Browsing by Author "Hashemi, M. S."

Now showing 1 - 7 of 7

A lie group approach to solve the fractional poisson equation
(Editura Academiei Romane, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Parto-Haghighi, M.
In the present paper, approximate solutions of fractional Poisson equation (FPE) have been considered using an integrator in the class of Lie groups, namely, the fictitious time integration method (FTIM). Based on the FTIM, the unknown dependent variable u(x, t) is transformed into a new variable with one more dimension. We use a fictitious time tau as the additional dimension (fictitious dimension), by transformation: v(x, t, tau) := (1 + tau)(k) u(x, t), where 0 < k <= 1 is a parameter to control the rate of convergency in the FTIM. Then the group preserving scheme (GPS) is used to integrate the new fractional partial differential equations in the augmented space R2+1. The power and the validity of the method are demonstrated using two examples.
Integrability, invariant and soliton solutions of generalized Kadomtsev-Petviashvili-modified equal width equation
(Elsevier Gmbh, Urban & Fischer verlag, 2017) Hashemi, M. S.; Baleanu, Dumitru; Haji-Badali, A.; Alizadeh, F.; Baleanu, D.; 56389
In this paper, the Painleve analysis is applied to test the integrability of the generalized Kadomtsev-Petviashvili-modified equal width (KP-MEW) equation with time dependent coefficients. Symmetry reductions and some corresponding invariant solutions in the integrable cases are completely considered. Soliton solutions of constant variables case in two integrable cases are reported. (C) 2017 Elsevier GmbH. All rights reserved.
Invariant Investigation on the System of Hirota-Satsuma Coupled KdV Equation
(Amer inst Physics, 2018) Hashemi, M. S.; Baleanu, Dumitru; Balmeh, Z.; Akgul, A.; Akgul, E. K.; Baleanu, D.; 56389
We show how invariant subspace method can be extended to the system time fractional differential equations and construct their exact solutions. Effectiveness of the method has been illustrated by the time fractional Hirota-Satsuma Coupled KdV(HSCKdV) equation.
Lie symmetry analysis and exact solutions of the time fractional gas dynamics equation
(NATL INST Optoelectronics, 2016) Baleanu, Dumitru; Baleanu, Dumitru
Finding the symmetries of a given fractional differential equation is a hot topic in the field of fractional differentiation and its applications. In this manuscript, the Lie symmetries of the time fractional gas dynamics (TFGD) equation are analyzed and new exact solutions are obtained.
Nonlinear Self-Adjointness and Nonclassical Solutions of A Population Model With Variable Coefficients
(Amer Scientific Publishers, 2018) Hashemi, M. S.; Baleanu, Dumitru; Inc, M.; Akgul, A.; Baleanu, D.; 56389
In this work, the size-structured population model with variable coefficients is considered to construct the exact solutions with nonclassical symmetries in the light of the heir equations. Nonlinear self-adjointness is shown and conservation laws are calculated too. Some scientific theorems have been given in this paper.
Numerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of line
(Academic Press inc Elsevier Science, 2016) Hashemi, M. S.; Baleanu, Dumitru; Baleanu, D.
We propose a simple and accurate numerical scheme for solving the time fractional telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate v is imposed onto the problem in order to transform the dependent variable u(x, t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of method of line and group preserving scheme (GPS) is proposed to find the approximate solutions. This method preserves the geometric structure of the problem. Power and accuracy of this method has been illustrated through some examples of TFT equation. (C) 2016 Elsevier Inc. All rights reserved.
On the Time Fractional Generalized Fisher Equation: Group Similarities and Analytical Solutions
(IOP Publishing LTD, 2016) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this letter, the Lie point symmetries of the time fractional Fisher (TFF) equation have been derived using a systematic investigation. Using the obtained Lie point symmetries, TFF equation has been transformed into a different nonlinear fractional ordinary differential equations with the Erdelyi-Kober fractional derivative which depends on the parameter a. After that some invariant solutions of underlying equation are reported.