Abstract
In this manuscript, we introduce a three dimension metric type spaces so called J-metric spaces. We prove the existence and uniqueness of a fixed point for self mappings in such spaces with different types of contractions. We use our result to prove the existence and uniqueness of a solution of the following fractional differential equations such as (P):{D(lambda)x(t) = f(t, x(t)) = Fx(t) if t is an element of I-0 = (0, T] x(0) = x(T) = r} . Moreover, we present other applications to systems of linear equations and Fredholm type integral equation.