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.


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)

1687-2770; 1687-2762

Document Type

Article - Journal

Document Version

Final Version

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Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

19 Mar 2022

Included in

Mathematics Commons