Ravi Agarwal, Snezhana Hristova, and Donal O’Regan
Proportional Caputo Fractional Differential Equations
Dynamic Systems and Applications 31 (2022) 89-104

https://doi.org/10.46719/dsa202231.02.02

ABSTRACT.
Practical stability properties of generalized proportional Caputo fractional delay differential equations are presented and exponential practical stability is introduced and studied. This type of stability on one hand is deeply connected with the used generalized proportional derivative and on the other hand it is a generalization of classical practical stability. Three types of sufficient conditions are obtained. Since the considered fractional derivative is a generalization of the Caputo fractional derivative, the connection with sufficient conditions in the literature concerning Caputo fractional differential equations is discussed. Some examples are given illustrate our theory.

AMS (MOS) Subject Classification. 34A08, 34D99.
Key Words and Phrases. Generalized proportional Caputo fractional derivative, fractional differential equations, exponential practical stability, Lyapunov functions.