Fixed point approach to solve fractional differential equations in S<sup>JS<sup>-metric spaces

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 different 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 differential equation $ \mathcal{(P)}:\left\{ \begin{array}{ccl} D^{\lambda}x(t) & = & f(t, x(t)) = Fx(t) \mbox{ if } t\in I_0 = (0, T] \\ x(0) & = & x(T) = r \ \end{array} \right\}. $ These applications show the effectiveness of our approach as a powerful tool for solving several types of differential equations.

Keywords

• fixed point
• s^js-metric spaces
• system of linear equations
• fractional differential equations