On fuzzy fractional Schrödinger equations under Caputo’s H-differentiability¹

Article type: Research Article

Authors: Wang, Yupin | Sun, Shurong^{; *} | Han, Zhenlai

Affiliations: School of Mathematical Sciences, University of Jinan, Jinan, Shandong, PR China

Correspondence: [*] Corresponding author. Shurong Sun, School of Mathematical Sciences, University of Jinan, Jinan 50022, Shandong, PR China. E-mail: [email protected].

Note: [1 ] This research is supported by the Natural Science Foundation of China(61703180), and supported by Shandong Provincial Natural Science Foundation(ZR2016AM17, ZR2017MA043).

Abstract: In this paper, we initiate to investigate the existence and uniqueness of solutions to initial value problems for fuzzy fractional Schrödinger equations involving the Caputo’s H-derivative. Continuous dependence on initial values of the solution is also considered. Our results are based on a successive approximation method and the Banach contraction mapping principle. Two examples are presented for our new results.

Keywords: Fuzzy fractional differential equation, Schrödinger equation, initial value problem, strongly generalized Hukuhara differentiability, fixed point theorem

DOI: 10.3233/JIFS-161474

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 6, pp. 3929-3940, 2018