]>
2016
9
11
ISSN 2008-1898
179
Residual power series method for time-fractional Schrödinger equations
Residual power series method for time-fractional Schrödinger equations
en
en
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).
5821
5829
Yu
Zhang
College of Mathematics and Information Science
North China University of Water Resources and Electric Power
China
Amit
Kumar
Department of Mathematics
National Institute of Technology
India
Sunil
Kumar
Department of Mathematics
National Institute of Technology
India
Dumitru
Baleanu
Department of Mathematics
Cankya University
Institute of Space Sciences
Turkey
Romania
Xiao-Jun
Yang
School of Mechanics and Civil Engineering
China University of Mining and Technology
China
dyangxiaojun@163.com
residual power series
fractional power series
Fractional Schrödinger equation
exact solution.
Article.10.pdf
[
[1]
S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys. Lett. A, 360 (2006), 109-113
##[2]
O. Abu Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, J. Adv. Res. Appl. Math., 5 (2013), 31-52
##[3]
A. A. Kilbas , H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North- Holland Mathematics Studies, Elsevier Science B.V.,, Amsterdam (2006)
##[4]
S. Kumar, A numerical study for the solution of time fractional nonlinear shallow water equation in oceans, Z. Naturforschung A, 68 (2013), 547-553
##[5]
S. Kumar, A new analytical modelling for fractional telegraph equation via Laplace transform, Appl. Math. Model., 38 (2014), 3154-3163
##[6]
S. Kumar, A. Kumar, D. Baleanu, Two analytical methods for time-fractional nonlinear coupled Boussinesq- Burger's equations arise in propagation of shallow water waves, Nonlinear Dynam., 85 (2016), 699-715
##[7]
A. Kumar, S. Kumar, M. Singh, Residual power series method for fractional Sharma-Tasso-Olever equation, Commun. Numer. Anal., 2016 (2016), 1-10
##[8]
S. Kumar, M. M. Rashidi, New analytical method for gas dynamic equation arising in shock fronts, Comput. Phys. Commun., 185 (2014), 1947-1954
##[9]
S. Momani, Z. Odibat, Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method, Appl. Math. Comput., 177 (2006), 488-494
##[10]
M. M. Mousaa, S. F. Ragab, Application of the homotopy perturbation method to linear and nonlinear schrödinger equations, Z. Naturforschung A, 63 (2008), 140-144
##[11]
Z. M. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 27-34
##[12]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, San Diego (1999)
##[13]
A. M. Wazwaz, A study on linear and nonlinear Schrödinger equations by the variational iteration method, Chaos Solitons Fractals, 37 (2008), 1136-1142
##[14]
X.-J. Yang, D. Baleanu, Fractal heat conduction problem solved by local fractional variation iteration method, Therm. Sci., 17 (2013), 625-628
##[15]
X.-J. Yang, D. Baleanu, M. P. Lazarevic, M. S. Cajic, Fractal boundary value problems for integral and differential equations with local fractional operators, Therm. Sci., 19 (2013), 959-966
##[16]
X.-J. Yang, D. Baleanu, H. M. Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press, Amsterdam (2016)
##[17]
X.-J. Yang, D. Baleanu, W.-P. Zhong, Approximate solutions for diffusion equations on Cantor space-time, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci., 14 (2013), 127-133
##[18]
X.-J. Yang, H. M. Srivastava, C. Cattani, Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics, Rom. Rep. Phys., 67 (2015), 752-761
##[19]
X.-J. Yang, J. A. Tenreiro Machado, D. Baleanu, C. Cattani, On exact traveling-wave solutions for local fractional Korteweg-de Vries equation, Chaos, 26 (2016), 1-5
]