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 F-metric space. The author derives some results for Suzuki-type contractions and orbitally T-complete and orbitally continuous mappings in 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 F-metric space.