A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included.
M. Bohner and S. Hristova, "Stability for Generalized Caputo Proportional Fractional Delay Integro-Differential Equations," Boundary Value Problems, vol. 2022, no. 1, article no. 14, SpringerOpen, Mar 2022.
The definitive version is available at https://doi.org/10.1186/s13661-022-01595-0
Mathematics and Statistics
Keywords and Phrases
Generalized Caputo Proportional Fractional Derivative; Initial Value Problem; Integro-Differential Fractional Equations; Variable Delays
International Standard Serial Number (ISSN)
Article - Journal
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19 Mar 2022