New approaches for the solution of space-time fractional Schrodinger equation

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Demir A., Bayrak M. A., Ozbilge E.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2020, no.1, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2020 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1186/s13662-020-02581-5
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Fractional Schrodinger equation, Residual power series method, Space-time fractional differential equations, DERIVATIVE OPERATOR, CALCULUS, DIFFUSION
  • Kocaeli University Affiliated: Yes

Abstract

The aim of this study is to establish the solution of the time-space fractional Schrodinger equation subject to initial and boundary conditions which has many applications in science such as nonlinear optics, plasma physics, super conductivity, based on the residual power series method (RPSM). We first apply suitable transformations to make the order of one of the fractional derivatives integer to implement the RPSM easily to construct the fractional power series solution. The method proposed in this article gives highly encouraging results. Illustrative examples show that this method is compatible with solving such fractional differential equations.