What question did this study set out to answer?

This research aims to explore Hyers–Ulam stability in nonlinear fractional hybrid dynamic equations across time scales.

May 15, 2026Open Access

Hyers–Ulam stability of a nonlinear fractional hybrid dynamic equations on arbitrary time scales via measures of noncompactness

Puntos clave

This research aims to explore Hyers–Ulam stability in nonlinear fractional hybrid dynamic equations across time scales.
Utilized measures of noncompactness and a generalized Darbo’s fixed-point theorem.
Established existence and uniqueness of solutions using the Banach fixed-point theorem.
Presented illustrative numerical examples to showcase the theoretical results.
Confirmed existence of solutions for nonlinear fractional hybrid dynamic equations.
Guaranteed uniqueness of solutions using Banach fixed-point theorem.
Demonstrated applicability of theoretical findings through numerical examples.

Resumen

This paper investigates different forms of Hyers–Ulam stability for solutions of a nonlinear fractional hybrid dynamic equation defined on arbitrary time scales. By employing the measure of noncompactness together with a newly developed generalized version of Darbo’s fixed-point theorem, the existence of solutions is established. The uniqueness of solutions is further guaranteed via the Banach fixed-point theorem. In addition, illustrative numerical examples are presented to demonstrate the applicability and effectiveness of the theoretical results.

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