Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions
Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan
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.
Topics & Concepts
MathematicsNonlinear systemScalar (mathematics)Lyapunov functionExponential stabilityStability (learning theory)Differential equationFractional calculusApplied mathematicsPartial differential equationMathematical analysisLyapunov exponentPhysicsComputer scienceMachine learningQuantum mechanicsGeometryFractional Differential Equations SolutionsAdvanced Control Systems DesignNonlinear Differential Equations Analysis