Autors: Madamlieva, E. B., Konstantinov M.
Title: On the Existence and Uniqueness of Solutions for Neutral-Type Caputo Fractional Differential Equations with Iterated Delays: Hyers–Ulam–Mittag–Leffler Stability
Keywords: Caputo-type fractional derivative, Hyers–Ulam–Mittag–Leffler stability, iterated delay

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.

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Issue

Mathematics, vol. 13, 2025, Switzerland, https://doi.org/10.3390/math13030484

Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus и Web of Science