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

Hasanen A. Hammad, Hassen Aydi^*, Nabil Mlaiki

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

Abstract

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, ηℷν-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.

Original language	English
Article number	97
Journal	Advances in Difference Equations
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13662-021-03255-6
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

2D Volterra integral equations
Atangana–Baleanu integral operators
Double controlled metric spaces
Riemann–Liouville fractional integrals

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10.1186/s13662-021-03255-6

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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",

abstract = "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, ηℷν-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.",

keywords = "2D Volterra integral equations, Atangana–Baleanu integral operators, Double controlled metric spaces, Riemann–Liouville fractional integrals",

author = "Hammad, {Hasanen A.} and Hassen Aydi and Nabil Mlaiki",

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AU - Hammad, Hasanen A.

AU - Aydi, Hassen

AU - Mlaiki, Nabil

PY - 2021/12

Y1 - 2021/12

N2 - 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, ηℷν-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.

AB - 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, ηℷν-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.

KW - 2D Volterra integral equations

KW - Atangana–Baleanu integral operators

KW - Double controlled metric spaces

KW - Riemann–Liouville fractional integrals

UR - http://www.scopus.com/inward/record.url?scp=85100271540&partnerID=8YFLogxK

U2 - 10.1186/s13662-021-03255-6

DO - 10.1186/s13662-021-03255-6

M3 - Article

AN - SCOPUS:85100271540

SN - 1687-1839

VL - 2021

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 97

ER -

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

Abstract

Keywords

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