Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

Hasanen A. Hammad; Hassen Aydi; Nabil Mlaiki

doi:10.1186/s13662-021-03255-6

$Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators$

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Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

Hasanen A. Hammad, Hassen Aydi and Nabil Mlaiki

Advances in difference equations, Vol.2021(1), pp.1-20

02/02/2021

DOI: https://doi.org/10.1186/s13662-021-03255-6

Abstract

Analysis

Difference and Functional Equations

Functional Analysis

general

Mathematics

Mathematics and Statistics

Ordinary Differential Equations

Partial Differential Equations

In this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, η ℷ ν -metric spaces) are obtained. Moreover, some related consequences dealing with a common fixed point concept and nontrivial examples to support our results are presented. Ultimately, we use the theoretical results to discuss the existence and uniqueness of solutions of 2D Volterra integral equations, Riemann–Liouville integrals and Atangana–Baleanu integral operators are given.

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Title: Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators
Creators - without role: Hasanen A. Hammad - Sohag University
Hassen Aydi - University of Sousse
Nabil Mlaiki - Prince Sultan University
Publication Details: Advances in difference equations, Vol.2021(1), pp.1-20
Publisher: Springer International Publishing
Identifiers: 9927007408331
Academic Unit: Prince Sultan University; Qassim University
Language: English
Resource Type: Journal article