Generalized Proportional Caputo Fractional Differential Equations with Delay and Practical Stability by the Razumikhin Method

Ravi Agarwal, Snezhana Hristova and Donal O’Regan
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Ravi Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Snezhana Hristova: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria
Donal O’Regan: School of Mathematical and Statistical Sciences, National University of Ireland, H91 TK33 Galway, Ireland

Mathematics, 2022, vol. 10, issue 11, 1-15

Abstract: Practical stability properties of generalized proportional Caputo fractional differential equations with bounded delay are studied in this paper. Two types of stability, practical stability and exponential practical stability, are defined and considered, and also some sufficient conditions to guarantee stability are presented. The study is based on the application of Lyapunov like functions and their generalized proportional Caputo fractional derivatives among solutions of the studied system where appropriate Razumikhin like conditions are applied (appropriately modified in connection with the fractional derivative considered). The theory is illustrated with several nonlinear examples.

Keywords: generalized proportional Caputo fractional derivative; differential equations; bounded delays; practical stability; Lyapunov functions; Razumikhin type conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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