Solvability of Fuzzy Partially Differentiable Models for Caputo–Hadamard-Type Goursat Problems Involving Generalized Hukuhara Difference - Si-Yuan Lin; Heng-You Lan; Ji-Hong Li (Fractal and Fractional)
In this paper, we investigate a class of fuzzy partially differentiable models for Caputo–Hadamard-type Goursat problems with generalized Hukuhara difference, which have been widely recognized as having a significant role in simulating and analyzing various kinds of processes in engineering and physical sciences. By transforming the fuzzy partially differentiable models into equivalent integral equations and employing classical Banach and Schauder fixed-point theorems, we establish the existence and uniqueness of solutions for the fuzzy partially differentiable models. Furthermore, in order to overcome the complexity of obtaining exact solutions of systems involving Caputo–Hadamard fractional derivatives, we explore numerical approximations based on trapezoidal and Simpson’s rules and propose three numerical examples to visually illustrate the main results presented in this paper.