Study of Uniqueness and Ulam-Type Stability of Abstract Hadamard Fractional Differential Equations of Sobolev Type via Resolvent Operators

Abstract

This paper focuses on studying the uniqueness of the mild solution for an abstract fractional differential equation. We use Banach’s fixed point theorem to prove this uniqueness. Additionally, we examine the stability properties of the equation using Ulam’s stability. To analyze these properties, we consider the involvement of Hadamard fractional derivatives. Throughout this study, we put significant emphasis on the role and properties of resolvent operators. Furthermore, we investigate Ulam-type stability by providing examples of partial fractional differential equations that incorporate Hadamard derivatives.

Keywords

• Hadamard fractional derivative
• Sobolev equation
• resolvent operators
• Ulam–Hyers–Rassias stability