Abstract
The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q-fractional Langevin differential equation with q-fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed q-fractional Langevin differential equation using the Banach contraction principle and Schaefer’s fixed-point theorem. We also elaborate on different kinds of Ulam stability. The theoretical outcomes are verified by examples.
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