Existence results and Ulam-Hyers stability for a sequential deformable fractional initial value problem
Articles > Article · 2026
Authors: LEILA SLIMANE, SOUAD AYADI, Özgür EGE, AHMAD ALOQAILY, NABIL MLAIKI
Journal of Inequalities and Applications, Journal Indexed in SCI Expanded, International, WoS, 2026, vol 2026, pp 1-12
DOI: 10.1186/s13660-026-03510-y
Summary
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.