Ulam-Hyers-Rassias stability of non-local problems for differential equations with Caputo fractional derivatives involving (non-delay) deviating arguments on unbounded intervals is investigated in [1]. By applying the Banach fixed-point theorem, we establish conditions for the existence and uniqueness of mild solutions within the space of continuous functions endowed with the Bielecki norm.

This kind of stability is important in applications where exact solutions are difficult to obtain and numerical or approximate solutions are commonly used. We emphasized that, in the analysis of UHR stability, the solution of the non-local problem depends on a function that satisfies the differential inequality. This result extends existing theory by establishing more generalized stability results for Caputo fractional differential equations with (non-delay) deviating arguments and non-local conditions on infinite domains.

[1] Dilna N., Langerova M. Ulam-Hyers-Rassias stability of Caputo fractional differential equations with deviating arguments on unbounded intervals, Mathematica Slovaca, 2026, to appear.