Ulam stability of fractional differential equations with a generalized Caputo derivative

Abstract

Studying the qualitative properties of solutions of dierential equations is one of the main topics in the eld of applied mathematics. Ulam stability is one of these properties. The objective of this paper is to extend Ulam-Hyers stability and Ulam-Hyers-Rassias stability theory to differential equations in the frame of a certain class of a generalized Caputo fractional derivative that comprises two parameters and demote to the Caputo and Caputo-Hadamard fractional derivatives when one of
these parameters approaches a certain value. We discuss the conditions a generalized Caputo frac-
tional dierential should satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To demonstrate our results we present some examples.