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384555

On a discussion of Volterra–Fredholm integral equation with discontinuous kernel

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Last updated: 29 Dec 2024

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Abstract

The purpose of this paper is to establish the general solution of a Volterra–Fredholm
integral equation with discontinuous kernel in a Banach space. Banach's fixed point
theorem is used to prove the existence and uniqueness of the solution. By using
separation of variables method, the problem is reduced to Volterra integral equations
of the second kind with continuous kernel. Normality and continuity of the integral
operator are also discussed.

DOI

10.1186/s42787-020-00074-8

Keywords

Banach space, Volterra–Fredholm integral equation, Separation of variables method

Authors

First Name

M.

Last Name

Abdou

MiddleName

A.

Affiliation

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Orcid

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First Name

A.

Last Name

Soliman

MiddleName

A.

Affiliation

Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

Email

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City

-

Orcid

-

First Name

M.

Last Name

Abdel–Aty

MiddleName

A.

Affiliation

Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

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City

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Orcid

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Volume

28

Article Issue

1

Related Issue

50535

Issue Date

2020-06-01

Receive Date

2024-10-07

Publish Date

2020-06-01

Page Start

1

Page End

10

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 28_Issue 1_Pages 1-10.pdf

PDF . 390.2kB

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https://joems.journals.ekb.eg/article_384555.html

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https://joems.journals.ekb.eg/service?article_code=384555

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384,555

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Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

On a discussion of Volterra–Fredholm integral equation with discontinuous kernel

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Article

Created At

21 Dec 2024