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

Abstract

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.

Keywords

• existence and uniqueness
• continuous dependence and ε-approximation
• coupled system of fuzzy fractional partial differential equations
• Banach fixed point theorem
• Gronwall inequality of the vector form