Existence Results for Integral Equations and Boundary Value Problems via Fixed Point Theorems for Generalized \(F\)-Contractions in \(b\)-Metric-Like Spaces

Abstract

In this paper, we introduce some new classes of generalized $F$-contractions and we establish certain fixed point results for such mappings in the setting of $b$-metric-like spaces. Some examples will illustrate the results and the corresponding computer simulations are suggestive from the output point of view. A second purpose of the paper is to apply the abstract results in the study of the existence of a solution for an integral equation problem and for a boundary value problem related to a real life mathematical model, namely, the problem of conversion of solar energy to electrical energy. Our study is concluded with an open problem, related to an integrodifferential equation arising in the study of electrical and electronics circuit analysis.