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Strict Stability of Fractional Differential Equations with a Caputo Fractional Derivative with Respect to Another Function

Author

Listed:
  • Ravi P. Agarwal

    (Emeritus Research Professor, Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA)

  • Snezhana Hristova

    (Faculty of Mathematics and Informatics, Plovdiv University, 4000 Plovdiv, Bulgaria)

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, Ireland)

Abstract

In this paper, we study nonlinear systems of fractional differential equations with a Caputo fractional derivative with respect to another function (CFDF) and we define the strict stability of the zero solution of the considered nonlinear system. As an auxiliary system, we consider a system of two scalar fractional equations with CFDF and define a strict stability in the couple. We illustrate both definitions with several examples and, in these examples, we show that the applied function in the fractional derivative has a huge influence on the stability properties of the solutions. In addition, we use Lyapunov functions and their CFDF to obtain several sufficient conditions for strict stability.

Suggested Citation

  • Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2025. "Strict Stability of Fractional Differential Equations with a Caputo Fractional Derivative with Respect to Another Function," Mathematics, MDPI, vol. 13(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:452-:d:1579740
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