Some new inequalities of Hermite Hadamard type via Katugampola fractional integral

Abstract

In this paper, our aim is to establish the control mechanism of the iteration process defined as S-iteration in the literature. First of all, it is to determine the dynamics of a system with chaotic property under Siteration. Afterward, we investigate the stability state of the chaotic system under this iteration with the parameters of the S-iteration. In addition, using the chaotic logistic system, we will illustrate the theoretical results in this example in the MATLAB program. Finally, we will examine the periodic state of the S-iteration and investigate the cases in which the periodic behavior is stable or unstable of the S-iteration with the Lyapunov exponent.