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 (US) of a Caputo q-fractional Langevin differential equation (FLDE) under q-fractional integral boundary conditions (FIBCs). 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 (BCP) for checking the existence and uniqueness of solutions of Caputo q- 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 UHS, GUHS, UHRS, and GUHRS. We validate our theoretical findings through illustrative examples.