Fixed point approach to solve fractional differential equations in $ S^{JS} $-metric spaces

Abstract

<abstract><p>This study aims to establish a new fixed point theorem in the framework of $ S^{JS} $-metric spaces, recently introduced by Beg et al. We propose different principles of contraction using various techniques. The theorems obtained represent a new framework for other future work in the considered space. Also, we provide two applications of our results to linear system of equations and the following fractional differential equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \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\}. $\end{document} </tex-math></disp-formula></p> <p>These applications show the effectiveness of our approach as a powerful tool for solving several types of differential equations.</p></abstract>