Work

Generalized Lipschitz Stability for Switched Differential Equations with Riemann–Liouville Fractional Derivatives with Respect to Another Function

Year: 2026

Type: article

Abstract: Switched fractional differential equations with Riemann–Liouville fractional derivatives with respect to another function (RLDFs) with orders between zero and one are studied. We provide a detailed algorithm for constructing the solution of the studied switched fractional system, and we illustrate with several examples the influence on both the switching rules and the applied function in the fractional derivative on the behavior of the solution. We define generalized Lipschitz stability in time for the studied system, and this type of stability guarantees that the solutions will be close to the initial values on intervals excluding the points of singularities, i.e., the initial time point and the switching time points. We prove auxiliary results for Lyapunov functions and their RLDFs, including quadratic Lyapunov functions. These results are applied to study generalized Lipschitz stability in time.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10070450

Authors: Snezhana Hristova, Donal O’Regan

Institutions: Plovdiv University, Ollscoil na Gaillimhe – University of Galway

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Bulgarian National Science Fund