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

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 21
• Main Authors: Demir, Ali, Bayrak, Mine Aylin, Ozbilge, Ebru
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 20.03.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary conditions; Control theory; Difference and Functional Equations; Differential equations; Fractional Schrödinger equation; Functional Analysis; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear optics; Ordinary Differential Equations; Partial Differential Equations; Plasma physics; Plasmas (physics); Power; Power series; Quantum physics; Residual power series method; Schrodinger equation; Space-time fractional differential equations; Spacetime; Space-time fractional differential equations; Fractional Schrödinger equation; Residual power series method
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02581-5

The aim of this study is to establish the solution of the time-space fractional Schrödinger 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.