Solution of Fractional Differential Equations Utilizing Symmetric Contraction

Abstract

The aim of this paper is to present another family of fractional symmetric $\alpha$ - $\eta$ -contractions and build up some new results for such contraction in the context of $\mathrm{ℱ}$ -metric space. The author derives some results for Suzuki-type contractions and orbitally $T$ -complete and orbitally continuous mappings in $\mathrm{ℱ}$ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in $\mathrm{ℱ}$ -metric space.