We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self-distance is not necessarily zero. For this, first we introduce a Ćirić type generalized F-contraction and F-Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate our results, we give throughout the paper some examples. © 2018, Semnan University, Center of Excellence in Nonlinear Analysis and Applications. All rights reserved.