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- Title
Existence, uniqueness, and stability analysis of fractional Langevin equations with anti‐periodic boundary conditions.
- Authors
Shah, Syed Omar; Rizwan, Rizwan; Xia, Yonghui; Zada, Akbar
- Abstract
This paper is devoted to studying the system of switched coupled implicit fractional Langevin equations of nonlinear form with anti‐periodic boundary conditions. In the first step, problem's equivalence and the corresponding integral equation by applying fractional calculus tools are established, and a fixed point problem is defined. For mixed monotone mappings, we have used coupled fixed point theorems to achieve the existence and uniqueness of solutions of these equations. In the next step, by using Banach's fixed point theorem, Ulam–Hyers, Ulam–Hyers–Rassias, generalized Ulam–Hyers and generalized Ulam–Hyers–Rassias stabilities of our considered model are discussed. An example is given at the end for the verification of our results.
- Subjects
LANGEVIN equations; FRACTIONAL calculus; NONLINEAR equations; EXISTENCE theorems; MATHEMATICAL mappings; INTEGRAL equations
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 17, p17941
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9539