Existence of solutions of integral and fractional differential equations using α-type rational F-contractions in metric-like spaces

Abstract

We present α-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly α-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain suffcient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.