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

Ravi P. Agarwal, Snezhana Hristova () and Donal O’Regan
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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

Mathematics, 2025, vol. 13, issue 3, 1-18

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.

Keywords: nonlinear fractional differential equations; Caputo fractional derivative with respect to another function; strict stability; Lyapunov functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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