Stability analysis of Caputo q-fractional Langevin differential equations under q-fractional integral conditions

The primary objective of the paper is exploring the Ulam stability $(\mathcal{US})$ of a Caputo q-fractional Langevin differential equation $(\mathcal{FLDE})$ under q-fractional integral boundary conditions $(\mathcal{FIBC}s)$ . The novelty of this work stands out for its broader generality compared to the existing research focused on the Caputo q-fractional derivative. We apply the Banach contraction principle $(\mathcal{BCP})$ for checking the existence and uniqueness of solutions of Caputo $q-\mathcal {FLD}$ equations. The framework of the study integrates fundamental principles from both fractional calculus and quantum calculus. Additionally, we discuss various forms of Ulam stability, namely $\mathcal{UHS}$ , $\mathcal{GUHS}$ , $\mathcal{UHRS}$ , and $\mathcal{GUHRS}$ . We validate our theoretical findings through illustrative examples.