Solutions of initial and boundary value problems via F-contraction mappings in metric-like space

Document Type : Research Paper


1 Department of Mathematics, Texas A & M University - Kingsville - 78363-8202, Texas, USA

2 Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007, Gujarat, India

3 Department of Mathematics, United Arab Emirates University, UAE


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 Ciric 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.