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On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

Author

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  • Dongming Nie
  • Azmat Ullah Khan Niazi
  • Bilal Ahmed

Abstract

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.

Suggested Citation

  • Dongming Nie & Azmat Ullah Khan Niazi & Bilal Ahmed, 2020. "On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:3276873
    DOI: 10.1155/2020/3276873
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