Periodic Solutions For Nonlinear Systems of Multiple Integro-differential Equations that Contain Symmetric Matrices with Impulsive Actions

Abstract

This paper examines a new nonlinear system of multiple integro-differential equations containing symmetric matrices with impulsive actions. The numerical-analytic method of ordinary differential equations and Banach fixed point theorem are used to study the existence, uniqueness and stability of periodic solutions of impulsive integro-differential equations with piecewise continuous functions. This study is based on the Hölder condition in which the ordering , and are real numbers between 0 and 1.

Numerical-analytic successive approximation method for the investigation of periodic solutions of nonlinear integro-differential systems with piecewise constant argument of generalized type

“…Numerous studies and research, such as those by Butris et al [2][3][4], Dorociakova et al [18], Guerfi et al [19], Mitropolsky et al [24], Perestyuk [27], Ronto et al [31], Shslapk [34], and Vakhobov [36], have focused on the treatment of both autonomous and non-autonomous periodic systems using integral and differential equations, encompassing both linear and nonlinear cases. These studies generally delve into the theory of periodic solutions and modern methodologies for addressing periodic differential equations with high precision.…”