Abstract
This study aims to establish a new fixed point theorem in the framework of S-JS-metric spaces, recently introduced by Beg et al. We propose di fferent principles of contraction using various techniques. The theorems obtained represent a new framework for other future work in the considered space. Also, we provide two applications of our results to linear system of equations and the following fractional di fferential equation
(P): {D lambda x(t) = f(t, x(t) = Fx(t) if t is an element of I0 = (0, T]
x(0) = x(T) = r}.
These applications show the effectiveness of our approach as a powerful tool for solving several types of di fferential equations.