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Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers

Author

Listed:
  • Zahra Eidinejad
  • Reza Saadati
  • Tofigh Allahviranloo
  • Farzad Kiani
  • Samad Noeiaghdam
  • Unai Fernandez-Gamiz
  • Abdellatif Ben Makhlouf

Abstract

In this paper, we consider a conformable fractional differential equation with a constant coefficient and obtain an approximation for this equation using the Radu–Mihet method, which is derived from the alternative fixed- point theorem. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers–Ulam-H-Fox stability for this equation. Finally, by providing numerical examples, we show the application of the obtained results.

Suggested Citation

  • Zahra Eidinejad & Reza Saadati & Tofigh Allahviranloo & Farzad Kiani & Samad Noeiaghdam & Unai Fernandez-Gamiz & Abdellatif Ben Makhlouf, 2022. "Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers," Complexity, Hindawi, vol. 2022, pages 1-26, December.
    • Handle: RePEc:hin:complx:5630187
    DOI: 10.1155/2022/5630187
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