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

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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.