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

Author

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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)

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.

Suggested Citation

  • Ekaterina Madamlieva & Mihail Konstantinov, 2025. "On the Existence and Uniqueness of Solutions for Neutral-Type Caputo Fractional Differential Equations with Iterated Delays: Hyers–Ulam–Mittag–Leffler Stability," Mathematics, MDPI, vol. 13(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:484-:d:1581292
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    References listed on IDEAS

    as
    1. Ekaterina Madamlieva & Mihail Konstantinov & Marian Milev & Milena Petkova, 2020. "Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2021. "Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
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