Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with $\mho$-Caputo Fractional Differential Equations

Year 2024, Volume: 7 Issue: 4, 187 - 198

Abduljawad Anwar

https://doi.org/10.33434/cams.1556314

Abstract

This paper examines the existence, uniqueness, and Ulam-Hyers stability of solutions to nonlinear $\mho$-fractional differential equations with boundary conditions with a $\mho$-Caputo fractional derivative. The acquired results for the suggested problem are validated using a novel technique and minimum assumptions about the function $f$. The analysis reduces the problem to a similar integral equation and uses Banach and Sadovskii fixed point theorems to reach the desired findings. Finally, the inquiry is demonstrated by illustrative example to validate the theoretical findings.

Keywords

Banach Contraction mapping, Caputo fractional derivative, $\mho$-Caputo fractional derivative, Fixed point theorem, Fractional differential equations, Stability analysis, Ulam-Hyers stability

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