Stability Results for Nonlinear Implicit ϑ-Caputo Fractional Differential Equations with Fractional Integral Boundary Conditions

Abstract

This article examines the necessary conditions for the unique existence of solutions to nonlinear implicit ϑ-Caputo fractional differential equations accompanied by fractional order integral boundary conditions. The analysis draws upon Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Furthermore, the circumstances leading to the attainment of Ulam–Hyers–Rassias forms of stability are established. An illustrative example is provided to demonstrate the derived findings.