Stability Analysis of Atangana-Baleanu Fractional Delay Differential Equations

Résumé

This work investigates the Ulam-Hyers and generalized Ulam-Hyers-Rassias stability of fractional delay differential equations involving the Atangana-Baleanu derivative with Mittag-Leffler kernel. Numerical simulations validate the theoretical results, showing close agreement between exact and approximate solutions and confirming bounded error behaviour. These findings demonstrate the effectiveness of the Atangana-Baleanu fractional delay framework for modelling systems with memory and delay, particularly in epidemiological and immune response applications.

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