A certain class of $\theta_{L}$-type non-linear operators and some related fixed point results

Abstract

This paper presents a systematic investigation of an extension of the developments concerning the θ -contractions, which were proposed in 2014 by Jleli and Samet. This paper generalizes the notion of the θ -contractions to the case of non-linear θ L -contraction mappings, and prove multi-valued fixed point results in b-metric-like spaces. The paper also includes a tangible example, which displays the motivation for such investigations as those presented here. This paper is completed by giving an application of the proposed non-linear θ L -contractions to the Liouville-Caputo fractional derivatives and fractional differential equations.