eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-10-01
4
4
261
275
5643
Solutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
Ahmad Neirameh
a.neirameh@gmail.com
1
Saeid Shokooh
shokooh.sd@gmail.com
2
Mostafa Eslami
mostafaeslami1@gmail.com
3
Department of Mathematics, faculty of Science, Gonbad Kavous University, Gonbad, Iran
Department of Mathematics, faculty of Science, Gonbad Kavous University, Gonbad, Iran
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
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.
http://cmde.tabrizu.ac.ir/article_5643_67059c561d0c6654f169bd004b37123b.pdf
Riccati equations
tanh method
Analytical solution
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-10-01
4
4
276
284
5645
On asymptotic stability of Prabhakar fractional differential systems
Mohammad Hossein Derakhshan
m.h.derakhshan.20@gmail.com
1
Mohammadreza Ahmadi Darani
ahmadi.darani@sci.sku.ac.ir
2
Alireza Ansari
alireza_1038@yahoo.com
3
Reza Khoshsiar Ghaziani
khoshsiar@sci.sku.ac.ir
4
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
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.
http://cmde.tabrizu.ac.ir/article_5645_de0b06fb29625a6c8d276eb9fc20e84a.pdf
Asymptotically stable
Prabhakar fractional derivative
Generalized Mittag-Leffer function
Riemann-Liouville fractional derivative
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-10-01
4
4
285
297
5644
Positive solutions for discrete fractional initial value problem
Tahereh Haghi
taherehhaghi@gmail.com
1
Kazem Ghanbari
kghanbari@sut.ac.ir
2
Sahand University of Technology, Tabriz, Iran
Sahand University of Technology, Tabriz, Iran
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.
http://cmde.tabrizu.ac.ir/article_5644_90f2bdba699867d7927f805399e1c7bf.pdf
discrete fractional calculus
existence of solutions
Positive solution, Fixed point theorem
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-10-01
4
4
298
308
5660
Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries
Elham Lashkarian
lashkarianelham@yahoo.com
1
Reza Hejazi
ra.hejazi@gmail.com
2
Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
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.
http://cmde.tabrizu.ac.ir/article_5660_9ecafe6aa9271d65c1fe9c2008211643.pdf
Wave equation
Symmetry
Similarity solution
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-10-01
4
4
309
322
5738
Application of high-order spectral method for the time fractional mobile/immobile equation
Hossein Pourbashash
h.pourbashash@ugsr.ir
1
Department of Mathematics, University of Garmsar, Garmsar-Iran
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.
http://cmde.tabrizu.ac.ir/article_5738_b83958c5c246fe0f1db8c9f6d51f6913.pdf
Time fractional
mobile/immobile (MIM) equation
finite difierence
spectral method
Legendre collocation method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-10-01
4
4
323
334
5821
An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions
Marzieh Khaksarfard
khaksarfard.m@gmail.com
1
Yadollah Ordokhani
ordokhani2000@yahoo.com
2
Esmail Babolian
babolian@khu.ac.ir
3
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
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.
http://cmde.tabrizu.ac.ir/article_5821_b2568988dc65b39325476c9da38f1f70.pdf
Radial basis functions
Heat conduction
Dirichlet and Neumann boundary Conditions