2016
4
4
4
74
Solutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
2
2
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.
1

261
275


Ahmad
Neirameh
Department of Mathematics, faculty of Science,
Gonbad Kavous University, Gonbad, Iran
Department of Mathematics, faculty of Science,
Gon
I. R. Iran
a.neirameh@gmail.com


Saeid
Shokooh
Department of Mathematics, faculty of Science,
Gonbad Kavous University, Gonbad, Iran
Department of Mathematics, faculty of Science,
Gon
I. R. Iran
shokooh.sd@gmail.com


Mostafa
Eslami
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Mathematical
I. R. Iran
mostafaeslami1@gmail.com
Riccati equations
tanh method
Analytical solution
On asymptotic stability of Prabhakar fractional differential systems
2
2
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 RiemannLiouville fractional derivatives is also given.
1

276
284


Mohammad Hossein
Derakhshan
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty
I. R. 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.
Department of Applied Mathematics, Faculty
I. R. 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
Department of Applied Mathematics, Faculty
I. R. Iran
alireza_1038@yahoo.com


Reza
Khoshsiar Ghaziani
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
khoshsiar@sci.sku.ac.ir
Asymptotically stable
Prabhakar fractional derivative
Generalized MittagLeffer function
RiemannLiouville fractional derivative
Positive solutions for discrete fractional initial value problem
2
2
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.
1

285
297


Tahereh
Haghi
Sahand University of Technology, Tabriz, Iran
Sahand University of Technology, Tabriz, Iran
I. R. Iran
taherehhaghi@gmail.com


Kazem
Ghanbari
Sahand University of Technology, Tabriz, Iran
Sahand University of Technology, Tabriz, Iran
I. R. Iran
kghanbari@sut.ac.ir
discrete fractional calculus
existence of solutions
Positive solution, Fixed point theorem
Polynomial and nonpolynomial solutions set for wave equation with using Lie point symmetries
2
2
This paper obtains the exact solutions of the wave equation as a secondorder partial differential equation (PDE). We are going to calculate polynomial and nonpolynomial 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.
1

298
308


Elham
Lashkarian
Department of Mathematical Sciences, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematical Sciences, Shahrood
I. R. Iran
lashkarianelham@yahoo.com


Reza
Hejazi
Department of Mathematical Sciences, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematical Sciences, Shahrood
I. R. Iran
ra.hejazi@gmail.com
Wave equation
Symmetry
Similarity solution
Application of highorder spectral method for the time fractional mobile/immobile equation
2
2
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.
1

309
322


Hossein
Pourbashash
Department of Mathematics, University of Garmsar, GarmsarIran
Department of Mathematics, University of
I. R. Iran
h.pourbashash@ugsr.ir
Time fractional
mobile/immobile (MIM) equation
finite difierence
spectral method
Legendre collocation method
An efficient approximate method for solution of the heat equation using LaguerreGaussians radial functions
2
2
In the present paper, a numerical method is considered for solving onedimensional 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 LaguerreGaussians (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.
1

323
334


Marzieh
Khaksarfard
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical
I. R. Iran
khaksarfard.m@gmail.com


Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical
I. R. Iran
ordokhani2000@yahoo.com


Esmail
Babolian
Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
Faculty of Mathematical Sciences and Computer,
Kha
I. R. Iran
babolian@khu.ac.ir
Radial basis functions
Heat conduction
Dirichlet and Neumann boundary Conditions