Ulam–Hyers and Generalized Ulam–Hyers Stability of Fractional Differential Equations with Deviating Arguments

Abstract

In this paper, we study the initial value problem for the fractional differential equation with multiple deviating arguments. By using Krasnoselskii’s fixed point theorem, the conditions of solvability of the problem are obtained. Furthermore, we establish Ulam–Hyers and generalized Ulam–Hyers stability of the fractional functional differential problem. Finally, two examples are presented to illustrate our results, one is with a pantograph-type equation and the other is numerical.

Keywords

• Caputo derivative
• Krasnoselskii’s fixed point theorem
• solvability
• UH stability
• GUH stability