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

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...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 11; no. 5; p. 686
Main Authors Abdeljawad, Thabet, Agarwal, Ravi P, Karapınar, Erdal, Kumari, P Sumati
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.05.2019
Subjects
Approximation
Computational mathematics
Differential equations
extended b-metric space
Fredholm equations
HR-Θ-contraction
Inequality
Integral equations
Metric space
nonlinear fractional differential equation of the Caputo type
nonlinear Volterra–Fredholm integral equations
Θe-contraction
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11050686