Qualitative Analyses of Integro-Fractional Differential Equations with Caputo Derivatives and Retardations via the Lyapunov–Razumikhin Method
Osman Tunç, Özkan Atan, Cemil Tunç, Jen‐Chih Yao
Abstract
The purpose of this paper is to investigate some qualitative properties of solutions of nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo fractional derivatives. These properties include uniform stability, asymptotic stability, Mittag–Leffer stability and boundedness. The presented results are proved by defining an appropriate Lyapunov function and applying the Lyapunov–Razumikhin method (LRM). Hence, some results that are available in the literature are improved for the FrRIDEs and obtained under weaker conditions via the advantage of the LRM. In order to illustrate the results, two examples are provided.
Topics & Concepts
MathematicsLyapunov functionFractional calculusStability (learning theory)Nonlinear systemExponential stabilityDifferential equationApplied mathematicsFunction (biology)Mathematical analysisComputer sciencePhysicsMachine learningEvolutionary biologyBiologyQuantum mechanicsFractional Differential Equations SolutionsAdvanced Control Systems DesignNonlinear Differential Equations Analysis