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354174

NON-OSCILLATORY BEHAVIOR OF HIGHER ORDER HILFER FRACTIONAL DIFFERENCE EQUATION

Article

Last updated: 29 Dec 2024

Subjects

-

Tags

Fractional Calculus operators

Abstract

In this paper, we look into the non-oscillatory behavior of the higher order forced fractional difference equation with positive and negative terms. Since the fractional difference and summation feature has considerably demonstrated its efficiency and validity due to its nonlocal nature and memory interpretation, we employ the Hilfer fractional difference operator, which is an extension of the most widely used Riemann-Liouville and Caputo fractional difference operators. Unlike the method that has been used in the literature, our study is based on certain fundamental concepts derived from discrete fractional calculus as well as mathematical inequalities. In order to aid in arriving at the important end result, a Volterra-type summation equation is constructed as a similar representation of our higher order Hilfer fractional difference problem. We were able to come up with new, easier to implement condition that were satisfied by the non-oscillatory solutions to our analyzed Hilfer fractional difference equation. Further, to demonstrate the empirical reliability of the theoretical finding, we lend a numerical example.

DOI

10.21608/jfca.2024.273085.1070

Keywords

Hilfer difference operator, non-oscillation criteria, mathematical inequalities, fractional difference equations

Authors

First Name

Sivakumar

Last Name

Arundhathi

MiddleName

-

Affiliation

Department of Mathematics, Periyar University, Salem-636 011, Tamilnadu, India

Email

arundhathiaks7@gmail.com

City

Salem

Orcid

-

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

2

Related Issue

44334

Issue Date

2024-07-01

Receive Date

2024-03-04

Publish Date

2024-07-01

Page Start

1

Page End

9

Print ISSN

2090-584X

Online ISSN

2090-5858

Link

https://jfca.journals.ekb.eg/article_354174.html

Detail API

https://jfca.journals.ekb.eg/service?article_code=354174

Order

354,174

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

NON-OSCILLATORY BEHAVIOR OF HIGHER ORDER HILFER FRACTIONAL DIFFERENCE EQUATION

Details

Type

Article

Created At

18 Dec 2024