期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 46, 期 1, 页码 438-460出版社
WILEY
DOI: 10.1002/mma.8520
关键词
boundary value problem; fractional differential equation; Ulam stability
The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) using the concept of Caputo fractional derivative. The existence and uniqueness of solutions for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. New sufficient conditions for ensuring the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of BVP-FDEs are also provided.
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 alpha is an element of(1,2)$$ \alpha \in \left(1,2\right) $$. 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.
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