A fixed point technique for solving boundary valuproblems in Branciari Suprametric Spaces

The technique to broaden the scope of fixed point theory is to extend the class of spaces that have stronger conceptual frameworks than metric spaces. Therefore, this paper explores the introduction of novel metric spaces, namely, Branciari suprametric spaces, and investigates some of its fundamental topological properties. An illustration is provided to validate the newly defined idea of Branciari suprametric spaces. Further two intriguing, fixed point results are proved, and a corollary is presented as an implication of our main result. The following is a specification of the analogue of the rectangle inequality in Branciari suprametric spaces d (ti,)£d (tn,)+d (ns,)+d (si,)+ md (t,n)d (n,s)d (s,i) B B B B B B B for all t ¹n, n ¹s and s ¹ i. Furthermore, by employing the results obtained, the present study intends to provide an appropriate solution for the nonlinear fractional differential equations of the Riemann-Liouville type.