R. I. Butt, J. Alzabut, M. Rehman, and J. M. Jonnalagadda. On Fractional Difference Langevin Equations Involving Non-Local Boundary Conditions. Dynamic Systems and Applications 29 (2020), No. 2, 305-326

https://doi.org/10.46719/dsa20202928

ABSTRACT.
In this paper, we study a fractional difference Langevin equation within nabla Caputo fractional difference and subject to non-local boundary conditions. The main results are proved by accommodating the newly defined discrete fractional calculus. The existence-uniqueness of solution is proved by Banach contraction principle. Besides, the existence of solutions is proved via Krasnoselskii and the nonlinear alternative Leray-Schauder fixed point theorems. The stability of solutions in sense of Ulam-Hyers is also established. We present a specific example to illustrate the applicability of our theoretical results.

AMS (MOS) Subject Classification. 39A30.

Key Words. Nabla Caputo fractional difference; Discrete Langevin equation; Non{local boundary conditions; Fixed point theorems; Existence and uniqueness theorems; Ulam-Hyers stability.