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226976

On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution

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Last updated: 05 Jan 2025

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Abstract

The devote of this paper is discussing the existence and uniqueness of fractional linear integro partial differential equation with
evolution kernel of heat type due to modified Bielecki method. In addition, Laplace homotopy perturbation method is used to
obtain the numerical solutions in the space 𝐶𝐸(𝐸 × [0, 𝑇]). Therefore, we estimate the error in different cases of 𝛼.

DOI

10.21608/bjas.2020.226976

Keywords

Fractional linear integro partial differential equation (FLIPDE), Caputo derivative, Riemann integral, Modified Bielecki method, Laplace homotopy perturbation method (LHPM)

Authors

First Name

M.A.

Last Name

Abdou

MiddleName

-

Affiliation

Mathematics Dept., Faculty of Education, Alexandria Univ., Benha, Egypt

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Orcid

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First Name

A.A.

Last Name

Soliman

MiddleName

-

Affiliation

Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt

Email

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Orcid

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First Name

M.H.

Last Name

Abdalla

MiddleName

-

Affiliation

Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt

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-

Orcid

-

First Name

F.A.

Last Name

Gawish

MiddleName

-

Affiliation

Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt

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Orcid

-

First Name

G.A.

Last Name

Mosa

MiddleName

-

Affiliation

Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt

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Volume

5

Article Issue

Issue 7 part (1) - (2)

Related Issue

20337

Issue Date

2020-10-01

Receive Date

2020-10-25

Publish Date

2020-10-01

Page Start

175

Page End

181

Print ISSN

2356-9751

Online ISSN

2356-976X

Article File

BJAS_Volume 5_Issue Issue 7 part (1) - (2)_Pages 175-181.pdf

PDF . 475.3kB

Link

https://bjas.journals.ekb.eg/article_226976.html

Detail API

https://bjas.journals.ekb.eg/service?article_code=226976

Order

29

Type

Original Research Papers

Type Code

1,647

Publication Type

Journal

Publication Title

Benha Journal of Applied Sciences

Publication Link

https://bjas.journals.ekb.eg/

MainTitle

On Existence and Uniqueness of Fractional Linear Integro Partial Differential Equation with Evolution Kernel Using Modified Bielecki Method and its Numerical Solution

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Article

Created At

23 Jan 2023