Innovative fixed point results on Istratescu type contractions with simulation function in b-metric spaces and applications

Abstract

In the present study, we extend the utilization of contractions to b-metric spaces by utilizing simulation functions. We will conduct research into the Istratescu type contractions, a type of contractions that have simulation functions produced in them, and we will demonstrate new fixed point solutions for this type. By doing this, we want to provide further light on the characteristics of b-metric spaces and contribute to the continued improvement of fixed point theory in this field. The results of this study are significant because they are supported by examples that are presented, giving concrete proof of their practical applications in the solution of exploring nonlinear integral equations of Caputo-Type and nonlinear fractional differential equations. This use case emphasizes the ability to change and the significance of our approach in solving complex mathematical problems in a variety of fields.