University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
4
2016
10
01
Solutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
261
275
EN
Ahmad
Neirameh
Department of Mathematics, faculty of Science,
Gonbad Kavous University, Gonbad, Iran
a.neirameh@gmail.com
Saeid
Shokooh
Department of Mathematics, faculty of Science,
Gonbad Kavous University, Gonbad, Iran
shokooh.sd@gmail.com
Mostafa
Eslami
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
mostafaeslami1@gmail.com
Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Riccati equations we obtain several analytical solutions for perturbed nonlinear fractional Schrodinger equation. The proposed technique enables a straightforward derivation of parameters of solitary solutions.
Riccati equations,tanh method,Analytical solution
http://cmde.tabrizu.ac.ir/article_5643.html
http://cmde.tabrizu.ac.ir/article_5643_67059c561d0c6654f169bd004b37123b.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
4
2016
10
01
On asymptotic stability of Prabhakar fractional differential systems
276
284
EN
Mohammad Hossein
Derakhshan
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
m.h.derakhshan.20@gmail.com
Mohammadreza
Ahmadi Darani
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran.
ahmadi.darani@sci.sku.ac.ir
Alireza
Ansari
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
alireza_1038@yahoo.com
Reza
Khoshsiar Ghaziani
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
khoshsiar@sci.sku.ac.ir
In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given.
Asymptotically stable,Prabhakar fractional derivative,Generalized Mittag-Leffer function,Riemann-Liouville fractional derivative
http://cmde.tabrizu.ac.ir/article_5645.html
http://cmde.tabrizu.ac.ir/article_5645_de0b06fb29625a6c8d276eb9fc20e84a.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
4
2016
10
01
Positive solutions for discrete fractional initial value problem
285
297
EN
Tahereh
Haghi
Sahand University of Technology, Tabriz, Iran
taherehhaghi@gmail.com
Kazem
Ghanbari
Sahand University of Technology, Tabriz, Iran
kghanbari@sut.ac.ir
In this paper, the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement .The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz function. We use the method of upper and lower solutions and Schauder fixed point theorem to obtain the main results.
discrete fractional calculus,existence of solutions,Positive solution, Fixed point theorem
http://cmde.tabrizu.ac.ir/article_5644.html
http://cmde.tabrizu.ac.ir/article_5644_90f2bdba699867d7927f805399e1c7bf.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
4
2016
10
01
Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries
298
308
EN
Elham
Lashkarian
Department of Mathematical Sciences, Shahrood University of Technology,
Shahrood, Semnan, Iran
lashkarianelham@yahoo.com
Reza
Hejazi
Department of Mathematical Sciences, Shahrood University of Technology,
Shahrood, Semnan, Iran
ra.hejazi@gmail.com
This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE). We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry. We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation. A generalized procedure for polynomial solution is presented and this extended to the construction of related polynomials.
Wave equation,Symmetry,Similarity solution
http://cmde.tabrizu.ac.ir/article_5660.html
http://cmde.tabrizu.ac.ir/article_5660_9ecafe6aa9271d65c1fe9c2008211643.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
4
2016
10
01
Application of high-order spectral method for the time fractional mobile/immobile equation
309
322
EN
Hossein
Pourbashash
Department of Mathematics, University of Garmsar, Garmsar-Iran
h.pourbashash@ugsr.ir
In this paper, a numerical eﬃcient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a ﬁnite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ2−γ) for 0 < γ < 1. Also, we introduce the Legendre and shifted Legendre polynomials for full discretization. The aim of this paper is to show that the spectral method based on the egendre polynomial is also suitable for the treatment of the fractional partial differential equations. Numerical examples conﬁrm the high accuracy of proposed scheme.
Time fractional,mobile/immobile (MIM) equation,finite difierence,spectral method,Legendre collocation method
http://cmde.tabrizu.ac.ir/article_5738.html
http://cmde.tabrizu.ac.ir/article_5738_b83958c5c246fe0f1db8c9f6d51f6913.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
4
2016
10
01
An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions
323
334
EN
Marzieh
Khaksarfard
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
khaksarfard.m@gmail.com
Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
ordokhani2000@yahoo.com
Esmail
Babolian
Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
babolian@khu.ac.ir
In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equations. The results of numerical experiments are presented to confirm the validity and applicability of the presented scheme.
Radial basis functions,Heat conduction,Dirichlet and Neumann boundary Conditions
http://cmde.tabrizu.ac.ir/article_5821.html
http://cmde.tabrizu.ac.ir/article_5821_b2568988dc65b39325476c9da38f1f70.pdf