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325655

On the oscillation of solutions of Ψ-Hilfer generalized proportional fractional differential equations

Article

Last updated: 29 Dec 2024

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Tags

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Abstract

In this piece of work, we examined the oscillatory behavior of the Ψ-Hilfer generalized proportional fractional differential equations. In the literature, several oscillation criteria are established using various kinds of fractional operators such as Conformable, Hadamard, Ψ-Riemann Liouville, Ψ-Caputo and generalized proportional fractional derivative interms of Riemann Liouville and Caputo settings. Under various conditions, we established some sufficient conditions for the solutions of the above problem to be oscillatory via the Ψ-Hilfer generalized proportional fractional derivative with respect to another function. With the help of Young's inequality and the Volterra integral equation, we developed new oscillation criteria for the above problem to be oscillatory. As a result of this study, we generalized and regained some existing results in the literature because of the suitable selection of the kernel Ψ. Also, we provided two examples to demonstrate the usefulness of our findings. In particular, one of the example shows that the equation has a non-oscillatory solution when the hypothesis fails.

DOI

10.21608/jfca.2023.233149.1034

Keywords

Oscillation criteria, Ψ-Hilfer generalized proportional fractional derivative, nonoscillatory solution

Authors

First Name

James

Last Name

Viji

MiddleName

-

Affiliation

Department of Mathematics, Periyar University, Salem - 636011, Tamil Nadu, India.

Email

vijimaths25@gmail.com

City

Salem

Orcid

0009-0003-1383-3933

First Name

Velu

Last Name

Muthulakshmi

MiddleName

-

Affiliation

Department of Mathematics, Periyar University, Salem, Tamil Nadu, India

Email

vmuthupu@gmail.com

City

Salem

Orcid

0000-0003-0125-5032

Volume

15

Article Issue

1

Related Issue

44333

Issue Date

2024-01-01

Receive Date

2023-09-01

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_325655.html

Detail API

https://jfca.journals.ekb.eg/service?article_code=325655

Order

1

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

On the oscillation of solutions of Ψ-Hilfer generalized proportional fractional differential equations

Details

Type

Article

Created At

18 Dec 2024