On the New Qualitative Results in Integro-Differential Equations With Caputo Fractional Derivative and Multiple Kernels and Delays

Abstract

In this paper, qualitative properties such as uniform stability (US), asymptotic stability (AS) and Mittag-Leffler stability (MLS) of trivial solution and boundedness of nonzero solutions of a system of non-linear fractional integrodelay differential equations (FFIDDEs) with Caputo fractional derivative, multiple kernels and multiple delays are investigated. Four new theorems including sufficient conditions are proved on these qualitative concepts of solutions. The established conditions depend upon the verification of the basic qualitative results of fractional calculus and our main results, which are proved via the Lyapunov-Razumikhin method (LRM). In the end, as numerical applications of the proved theorems, an example is given to demonstrate the effectiveness of the applied method and obtained results. Our results improve and generalize the known ones in this direction.