Stability of Nonlinear Implicit Differential Equations with Caputo–Katugampola Fractional Derivative

Qun Dai and Yunying Zhang ()
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Qun Dai: School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China
Yunying Zhang: School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China

Mathematics, 2023, vol. 11, issue 14, 1-12

Abstract: The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equation is proved, and the relevant conclusions about the stability of Ulam–Hyers are obtained. Finally, the correctness of the conclusions is verified by an example.

Keywords: Caputo–Katugampola fractional derivative; Gronwall inequality; Banach fixed-point theorem; Ulam–Hyers stability; Ulam–Hyers–Rassias stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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