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Keywords = HR-Θ-contraction

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18 pages, 440 KB  
Article
Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space
by Thabet Abdeljawad, Ravi P Agarwal, Erdal Karapınar and P Sumati Kumari
Symmetry 2019, 11(5), 686; https://doi.org/10.3390/sym11050686 - 18 May 2019
Cited by 203 | Viewed by 6572
Abstract
The present paper aims to define three new notions: Θ e -contraction, a Hardy–Rogers-type Θ -contraction, and an interpolative Θ -contraction in the framework of extended b-metric space. Further, some fixed point results via these new notions and the study endeavors toward [...] Read more.
The present paper aims to define three new notions: Θ e -contraction, a Hardy–Rogers-type Θ -contraction, and an interpolative Θ -contraction in the framework of extended b-metric space. Further, some fixed point results via these new notions and the study endeavors toward a feasible solution would be suggested for nonlinear Volterra–Fredholm integral equations of certain types, as well as a solution to a nonlinear fractional differential equation of the Caputo type by using the obtained results. It also considers a numerical example to indicate the effectiveness of this new technique. Full article
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