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http://dx.doi.org/10.5666/KMJ.2018.58.4.651

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

Nashine, Hemant Kumar (Department of Mathematics, Texas A & M University - Kingsville)
Kadelburg, Zoran (University of Belgrade, Faculty of Mathematics)
Agarwal, Ravi P. (Department of Mathematics, Texas A & M University - Kingsville)
Publication Information
Kyungpook Mathematical Journal / v.58, no.4, 2018 , pp. 651-675 More about this Journal
Abstract
We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-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 ${\alpha}$-admissible mapping; F-contraction; integral equation; fractional differential equation;
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