Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions

Ravi Agarwal; Snezhana Hristova; Donal O’regan

doi:10.3390/fractalfract6010034

Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions

Ravi Agarwal, Snezhana Hristova, Donal O’regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

29 Citations (Scopus)

Abstract

In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fractional differential equation with the GPFD is considered as a comparison equation, and some comparison results are proven. Sufficient conditions for stability and asymptotic stability were obtained. Examples illustrating the results and ideas in this paper are also provided.

Original language	English
Article number	34
Journal	Fractal and Fractional
Volume	6
Issue number	1
DOIs	https://doi.org/10.3390/fractalfract6010034
Publication status	Published - Jan 2022

Keywords

Asymptotic stability
Fractional differential equations
Generalized proportional Caputo fractional derivative
Lyapunov functions
Stability

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10.3390/fractalfract6010034

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title = "Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions",

abstract = "In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fractional differential equation with the GPFD is considered as a comparison equation, and some comparison results are proven. Sufficient conditions for stability and asymptotic stability were obtained. Examples illustrating the results and ideas in this paper are also provided.",

keywords = "Asymptotic stability, Fractional differential equations, Generalized proportional Caputo fractional derivative, Lyapunov functions, Stability",

author = "Ravi Agarwal and Snezhana Hristova and Donal O{\textquoteright}regan",

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AU - Hristova, Snezhana

AU - O’regan, Donal

PY - 2022/1

Y1 - 2022/1

N2 - In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fractional differential equation with the GPFD is considered as a comparison equation, and some comparison results are proven. Sufficient conditions for stability and asymptotic stability were obtained. Examples illustrating the results and ideas in this paper are also provided.

AB - In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fractional differential equation with the GPFD is considered as a comparison equation, and some comparison results are proven. Sufficient conditions for stability and asymptotic stability were obtained. Examples illustrating the results and ideas in this paper are also provided.

KW - Asymptotic stability

KW - Fractional differential equations

KW - Generalized proportional Caputo fractional derivative

KW - Lyapunov functions

KW - Stability

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ER -

Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions

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Keywords

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