On Goursat problem for fuzzy delay fractional hyperbolic partial differential equations

In this paper, we consider Goursat boundary value problems for fuzzy delay fractional partial differential equations under Caputo gH-derivatives. Firstly, the unique solvability of the problems in finite domain is considered. Secondly, by restricting the force function and boundary conditions by exponential growth and using fixed point approach, the existence and the Ulam-Hyers stability of fuzzy mild solutions of the problem in infinite domain are investigated in two types with different geometric behaviors. It is necessary to implement that in many engineering applications, e.g. numerical solutions of a fuzzy dynamical system, the object of optimization problems or the trajectory of a economical dynamics etc., where finding the exact solution is more difficult than solving its approximate solutions, Ulam-Hyers stability is quite useful. Finally, as usual some examples are given to illustrate the obtained theoretical results.