On a class of langevin equations in the frame of caputo function-dependent-kernel fractional derivatives with antiperiodic boundary conditions
AIMS Mathematics, ISSN: 2473-6988, Vol: 6, Issue: 6, Page: 5518-5534
2021
- 17Citations
- 3Captures
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Article Description
In this manuscript, we consider a class of nonlinear Langevin equations involving two different fractional orders in the frame of Caputo fractional derivative with respect to another monotonic function ϑ with antiperiodic boundary conditions. The existence and uniqueness results are proved for the suggested problem. Our approach is relying on properties of ϑ-Caputo’s derivative, and implementation of Krasnoselskii’s and Banach’s fixed point theorem. At last, we discuss the Ulam-Hyers stability criteria for a nonlinear fractional Langevin equation. Some examples justifying the results gained are provided. The results are novel and provide extensions to some of the findings known in the literature.
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