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345429

SOME RESULTS ON NONLINEAR FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH POSITIVE CONSTANT COEFFICIENT

Article

Last updated: 29 Dec 2024

Subjects

-

Tags

Fractional order Differential Equations

Abstract

In this paper, we study the main results of existence and uniqueness of solutions of fractional Volterra integrodifferential equation involving Caputo fractional derivative of special class $n − 1 < \alpha \leq n, n > 1$. Also, uniqueness of solutions without the existence part and estimate on the solution were discussed. Furthermore, the various type of dependency of solutions of the proposed problem have been studied such as dependence on given initial data, continuously depends on the functions involved in the right side of the problem and on real parameters. The result of existence and uniqueness is obtained with help of well known Banach contraction principle and the integral inequality established by B. G. Pachpatte which provides explicit bound on the unknown function. Authors considered a class of special equations where singularities are removed and we are free to use general integral inequalities to discuss the various properties of solutions. This study may be the new motivation towards the class of more general type.The obtained some results are illustrated through example.

DOI

10.21608/jfca.2024.239746.1041

Keywords

Fractional integrodifferential equation, Existence and uniqueness of solution, Fixed point theorem, Integral inequality

Authors

First Name

Haribhau

Last Name

Tidke

MiddleName

Laxman

Affiliation

Department of Mathematics KBCNMU, Jalgaon

Email

tharibhau@gmail.com

City

Jalgaon

Orcid

-

First Name

Vinod

Last Name

Kharat

MiddleName

V

Affiliation

Department of Mathematics, N. B. Navale Sinhgad College of Engineering, Kegaon, Solapur

Email

vvkvinod9@gmail.com

City

Solapur

Orcid

-

Volume

15

Article Issue

1

Related Issue

44333

Issue Date

2024-01-01

Receive Date

2023-09-30

Publish Date

2024-01-01

Page Start

1

Page End

15

Print ISSN

2090-584X

Online ISSN

2090-5858

Link

https://jfca.journals.ekb.eg/article_345429.html

Detail API

https://jfca.journals.ekb.eg/service?article_code=345429

Order

8

Type

Regular research papers

Type Code

2,646

Publication Type

Journal

Publication Title

Journal of Fractional Calculus and Applications

Publication Link

https://jfca.journals.ekb.eg/

MainTitle

SOME RESULTS ON NONLINEAR FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH POSITIVE CONSTANT COEFFICIENT

Details

Type

Article

Created At

18 Dec 2024