On the Existence and Uniqueness of Solutions for Neutral-Type Caputo Fractional Differential Equations with Iterated Delays: Hyers–Ulam–Mittag–Leffler Stability

Ekaterina Madamlieva () and Mihail Konstantinov
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Ekaterina Madamlieva: Department of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1756 Sofia, Bulgaria
Mihail Konstantinov: Department of Mathematics, Faculty of Transportation Engineering, University of Architecture, Civil Engineering and Geodesy, 1046 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: This study investigates nonlinear Caputo-type fractional differential equations with iterated delays, focusing on the neutral type. Initially formulated by D. Bainov and the second author of the current paper between 1972 and 1978, these superneutral equations have been extensively studied in scholarly inquiry. The present research seeks to reinvigorate interest in such delays within sophisticated frameworks of differential equations, particularly those involving fractional calculus. The primary objectives are to thoroughly examine neutral-type fractional differential equations with iterated delays and provide novel insights into their existence and uniqueness by applying Bielecki’s and Chebyshev’s norms for solution constraints analysis. Additionally, this work establishes Hyers–Ulam–Mittag–Leffler stability for these equations.

Keywords: Caputo-type fractional derivative; iterated delay; Hyers–Ulam–Mittag–Leffler stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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