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

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 s...

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Bibliographic Details
Main Authors: Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/3/452
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Summary: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.
ISSN:2227-7390