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

Abstract 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.

# Mathematics # Deformable derivative # Fractional differential equation # Mild solution # Ulam-Hyers stability # Fixed point

Leila Slimane, Souad Ayadi, Ozgur Ege, et al. (2026). "Existence results and Ulam-Hyers stability for a sequential deformable fractional initial value problem". Journal of Inequalities and Applications. https://doi.org/10.1186/s13660-026-03510-y