STABILITY ANALYSIS FOR A CLASS OF FUZZY FRACTIONAL DIFFERENTIAL EQUATIONS WITH TIME DELAY INVOLVING GENERALIZED ATANGANA-BALEANU DERIVATIVE

Abstract

This research delves into a comprehensive investigation of a specific category of fuzzy fractional differential equations, focusing on issues of existence, uniqueness, and Ulam-Hyers stability of solutions. The considered equation incorporate the generalized Atangana-Baleanu derivative in the Caputo sense and encompass time-delays. Integral to the derivation of substantial results are functional analysis techniques, notably the Schaefer fixed point theorem for establishing existence and the Banach fixed point theorem for ensuring uniqueness. The study further extends its contributions by examining Ulam-Hyers stability concerning variations in parameters, encompassing both initial conditions or parameters of the equation. These insights are grounded in the application of generalized forms of Gronwall’s inequality. To illustrate and reinforce the obtained results, the research includes a demonstrative example