Some Stability Results and Existence of Solutions for a Backward Differential Equation with Time Advance via ζ—Caputo Fractional Derivative - Abdellatif Ben Makhlouf; Lassaad Mchiri; Mohamed Rhaima (Axioms, 2023)
In this paper, using a fixed point method, we proved the existence and uniqueness of solutions for a backward differential equation with time advance via <semantics>ζ−</semantics>Caputo fractional derivative. Furthermore, the Ulam–Hyers–Rassias and the Ulam–Hyers stabilities of the backward differential equation with time advance via <semantics>ζ−</semantics>Caputo fractional derivative are investigated. Finally, some experiments are given to illustrate the theoretical results.