A Fuzzy Solutions of Fractional-Integer Partial Differential Equations

The differential (integral) theory of fuzzy number value function based on the theory of fuzzy number space is one of the main research contents of fuzzy analysis, especially the fuzzy differential equation and integral equation, which are widely used in engineering technology and social science, have aroused great interest of scholars in different fields. The research of fuzzy differential equation is mainly based on the following three methods: The first is based on the H-derivative and the generalized derivative of Bede; The second is based on the extension principle of Zadeh; The third is based on the theory of differential inclusion, and the theory of fuzzy differential equations in these three meanings is different from each other. In this work, on the basis of H-derivative and the generalized derivative of Bede, the solutions of several kinds of classical partial differential equations are extended, and the existence of solutions of several types of fuzzy fractional and integer order partial differential equations are systematically studied.