Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters. (31st October 2020)

• Record Type: Journal Article
• Authors: Luo, Danfeng; Luo, Zhiguo; Qiu, Hongjun
• Other Names: Shaikhet Leonid Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-10-31
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/9372406
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper focuses on a kind of mixed fractional-order nonlinear delay difference equations with parameters. Under some new criteria and by applying the Brouwer theorem and the contraction mapping principle, the new existence and uniqueness results of the solutions have been established. In addition, we deduce that the solution of the addressed equation is Hyers–Ulam stable. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results.