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Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

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  • Danfeng Luo
  • Zhiguo Luo
  • Hongjun Qiu

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.

Suggested Citation

  • Danfeng Luo & Zhiguo Luo & Hongjun Qiu, 2020. "Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, October.
    • Handle: RePEc:hin:jnlmpe:9372406
    DOI: 10.1155/2020/9372406
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    Cited by:

    1. Abdelkrim Salim & Jehad Alzabut & Weerawat Sudsutad & Chatthai Thaiprayoon, 2022. "On Impulsive Implicit ψ -Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation," Mathematics, MDPI, vol. 10(24), pages 1-20, December.

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