On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Abstract

This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures the uniqueness of the solutions, while Schauder’s fixed-point theorem (SFPT) is instrumental in determining the existence of these solutions. Furthermore, we assess the stability of the proposed equation using the Ulam–Hyers stability criterion. To illustrate our results, we provide a concrete example showcasing their practical implications.

Keywords

• existence and uniqueness
• Ψ-Caputo fractional derivative
• fixed-point theorems