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Hyers-Ulam stability for boundary value problem of fractional differential equations with κ-Caputo fractional derivative

Authors: 

Ho Vu, John M. Rassias, Ngo Van Hoa

Source title: 
Mathematical Methods in the Applied Science, 2022 (ISI)
Academic year of acceptance: 
2021-2022
Abstract: 

The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) via the concept of Caputo fractional derivative with respect to another function with the order a. The existence and uniqueness results of a solution for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide new sufficient conditions to guarantee the Hyers-Ulam stability and the Hyers–Ulam–Rassias stability of BVP-FDEs. Furthermore, some concrete examples to consolidate the obtained results are also considered.