Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

• Published in: Fractal and fractional Vol. 6; no. 3; p. 132
• Main Authors: Zhang, Fan, Xu, Hai-Yang, Lan, Heng-You
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2022
• Subjects: Banach fixed point theorem; Boundary value problems; Cauchy problems; continuous dependence and ε-approximation; coupled system of fuzzy fractional partial differential equations; Decision making; existence and uniqueness; Existence theorems; Fixed points (mathematics); Fuzzy sets; Gronwall inequality of the vector form; Mathematical analysis; Ordinary differential equations; Partial differential equations; Science; Uniqueness
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract6030132

The purpose of this paper is to investigate a class of initial value problems of fuzzy fractional coupled partial differential equations with Caputo gH-type derivatives. Firstly, using Banach fixed point theorem and the mathematical inductive method, we prove the existence and uniqueness of two kinds of gH-weak solutions of the coupled system for fuzzy fractional partial differential equations under Lipschitz conditions. Then we give an example to illustrate the correctness of the existence and uniqueness results. Furthermore, because of the coupling in the initial value problems, we develop Gronwall inequality of the vector form, and creatively discuss continuous dependence of the solutions of the coupled system for fuzzy fractional partial differential equations on the initial values and ε-approximate solution of the coupled system. Finally, we propose some work for future research.