
doi: 10.3390/math11092132
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.
Langevin equations; fractional <i>q</i>-differential equation; Caputo derivative; green function; Ulam stability, Ulam stability, QA1-939, fractional <i>q</i>-differential equation, Langevin equations, green function, Caputo derivative, Mathematics
Langevin equations; fractional <i>q</i>-differential equation; Caputo derivative; green function; Ulam stability, Ulam stability, QA1-939, fractional <i>q</i>-differential equation, Langevin equations, green function, Caputo derivative, Mathematics
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