# Residual power series method for time-fractional Schrödinger equations

Volume 9, Issue 11, pp 5821--5829
• 1145 Views ### Authors

Yu Zhang - College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450000, China. Amit Kumar - Department of Mathematics, National Institute of Technology, Jamshedpur-831014, Jharkhand, India. Sunil Kumar - Department of Mathematics, National Institute of Technology, Jamshedpur-831014, Jharkhand, India. Dumitru Baleanu - Department of Mathematics, Cankya University, Ogretmenler Cad. 14, Balgat-06530, Ankara, Turkey. - Institute of Space Sciences, Magurele-Bucharest, Romania. Xiao-Jun Yang - School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.

### Abstract

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).

### Keywords

• residual power series
• fractional power series
• Fractional Schrödinger equation
• exact solution.

•  47H10
•  26A33
•  34A08
•  34A34

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