Existence results and Ulam-Hyers stability for a sequential deformable fractional initial value problem

In this study, we establish existence and Ulam-Hyers results for nonlinear sequential fractional differential equations involving the deformable derivative. We employ the Banach contraction principle and Krasnoselskii’s theorem to achieve these results. A key novelty of this work lies in the use of a sequential application of the deformable derivative, which yields a richer mathematical structure compared to single-order formulations. The theoretical findings are illustrated through a concrete example, and the practical relevance of the results is discussed in the context of stability analysis for dynamical systems modeled by deformable fractional equations.