Existence and Stability Analysis of Anti-Periodic Boundary Value Problems with Generalized Tempered Fractional Derivatives

Ricardo Almeida () and Natália Martins
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Ricardo Almeida: Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Natália Martins: Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2025, vol. 13, issue 19, 1-15

Abstract: In this study, we investigate implicit fractional differential equations subject to anti-periodic boundary conditions. The fractional operator incorporates two distinct generalizations: the Caputo tempered fractional derivative and the Caputo fractional derivative with respect to a smooth function. We investigate the existence and uniqueness of solutions using fixed-point theorems. Stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias is also considered. Three detailed examples are presented to illustrate the applicability and scope of the theoretical results. Several existing results in the literature can be recovered as particular cases of the framework developed in this work.

Keywords: fractional calculus; implicit fractional differential equations; anti-periodic boundary conditions; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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