Residual power series method for time-fractional Schrödinger equations

In this paper, the residual power series method (RPSM) is effectively applied to find the exact solutions of fractional-order time dependent Schrödinger equations. The competency of the method is examined by applying it to the several numerical examples. Mainly, we find that our solutions obtained by the proposed method are completely compatible with the solutions available in the literature. The obtained results interpret that the proposed method is very effective and simple for handling different types of fractional differential equations (FDEs). c ©2016 All rights reserved.

[1]  Dumitru Baleanu,et al.  On exact traveling-wave solutions for local fractional Korteweg-de Vries equation. , 2016, Chaos.

[2]  Shaher Momani,et al.  Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method , 2006, Appl. Math. Comput..

[3]  Xiao‐Jun Yang,et al.  Fractal boundary value problems for integral and differential equations with local fractional operators , 2013 .

[4]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[5]  Dumitru Baleanu,et al.  Two analytical methods for time-fractional nonlinear coupled Boussinesq–Burger’s equations arise in propagation of shallow water waves , 2016 .

[6]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[7]  Sunil Kumar,et al.  A new analytical modelling for fractional telegraph equation via Laplace transform , 2014 .

[8]  Abu Arqub,et al.  Series Solution of Fuzzy Differential Equations under Strongly Generalized Differentiability , 2013 .

[9]  Sunil Kumar,et al.  New analytical method for gas dynamics equation arising in shock fronts , 2014, Comput. Phys. Commun..

[10]  S. Abbasbandy THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER , 2006 .

[11]  H. Srivastava,et al.  THEORY AND APPLICATIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS. NORTH-HOLLAND MATHEMATICS STUDIES , 2006 .

[12]  I. Podlubny Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[13]  H. Srivastava,et al.  Local Fractional Integral Transforms and Their Applications , 2015 .

[14]  Saudi Arabia,et al.  APPROXIMATE SOLUTIONS FOR DIFFUSION EQUATIONS ON CANTOR SPACE-TIME , 2013 .

[15]  Sunil Kumar,et al.  Residual power series method for fractional Sharma-Tasso-Olever equation , 2016 .

[16]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[17]  A. Wazwaz A study on linear and nonlinear Schrodinger equations by the variational iteration method , 2008 .

[18]  Sunil Kumar A Numerical Study for the Solution of Time Fractional Nonlinear Shallow Water Equation in Oceans , 2013 .

[19]  Xiao‐Jun Yang,et al.  Fractal heat conduction problem solved by local fractional variation iteration method , 2013 .

[20]  Application of the Homotopy Perturbation Method to Linear and Nonlinear Schrödinger Equations , 2008 .