Extremal solutions of fuzzy fractional differential equations with $\psi$-Caputo derivative via monotone iterative method

Abstract

In this paper, using the monotone iterative technique combined with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of fuzzy fractional differential equations (FFDEs) with time-delays involving the $\psi$-Caputo derivative. Also, with aid of generalized Gr$\ddot{o}$nwall inequality, we investigative the Hyers-Ulam stability of solution for the system under consideration. Lately, two examples are provided to illustrate the theoretical results.