Existence of Solutions of Integral and Fractional Differential Equations Using α-type Rational F-contractions in Metric-like Spaces

Hemant Kumar Nashine; Zoran Kadelburg; Ravi P. Agarwal

doi:10.5666/KMJ.2018.58.4.651

Articles

Kyungpook Mathematical Journal 2018; 58(4): 651-675

Published online December 31, 2018

Existence of Solutions of Integral and Fractional Differential Equations Using α-type Rational F-contractions in Metric-like Spaces

Hemant Kumar Nashine, Zoran Kadelburg^∗, Ravi P. Agarwal

Department of Mathematics, Texas A & M University - Kingsville - 78363-8202, Texas, USA
e-mail : drhknashine@gmail.com
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, India
e-mail : hemant.nashine@vit.ac.in

University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia
e-mail : kadelbur@matf.bg.ac.rs

Department of Mathematics, Texas A & M University - Kingsville - 78363-8202, Texas, USA
e-mail : agarwal@tamuk.edu

Received: September 4, 2017; Revised: August 8, 2018; Accepted: August 13, 2018

Abstract

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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 sufficient 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.

Keywords: metric-like space, weakly α-admissible mapping, F-contraction, integral equation, fractional differential equation.