New Fixed Point Theorems in Orthogonal F -Metric Spaces with Application to Fractional Differential Equation

We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.This work was supported by the Basque Government under the Grant IT 1207-19