Modified Ulam-Hyers-Rassias Stability Analysis of Caputo Impulsive Fractional Delay Differential Equations

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DOI: https://doi.org/10.28924/2291-8639-24-2026-208
Published: Jul 6, 2026
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Wisdom Kevin Udogworen, Reny George, Modified Ulam-Hyers-Rassias Stability Analysis of Caputo Impulsive Fractional Delay Differential Equations, Int. J. Anal. Appl., 24 (2026), 208.

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Wisdom Kevin Udogworen, Reny George

Abstract

This article discuss the stability analysis of Caputo impulsive fractional delay differential equations using a modified Ulam-Hyers-Rassias stability approach. The effect of perturbations is intrinsically time-dependent due to its nonlocal and memory-dependent nature. The modified Ulam-Hyers-Rassias stability is crucial to fractional calculus. The real-valued function's integrability permits the inclusion of variable perturbations rather than a constant and guarantees that the stability inequality stays well-defined in the fractional situation. Therefore, compared to the classical Ulam-Hyers-Rassias stability technique, the modified approach offers a more realistic and general framework in fractional calculus. The findings contribute to improving the qualitative properties of fractional differential equations with delay factors, impulse disturbances, and memory effects.

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