Quaternion Fractional Difference with Quaternionic Fractional Order and Applications to Fractional Difference Equation

Chao Wang; Weiyu Xie; Ravi P. Agarwal

doi:10.2478/auom-2024-0015

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Quaternion Fractional Difference with Quaternionic Fractional Order and Applications to Fractional Difference Equation

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 32 (2024): Issue 1 (April 2024)

By: Chao Wang, Weiyu Xie and Ravi P. Agarwal

Open Access

|May 2024

Abstract

In this paper, we introduce the basic notions of the fractional summation, difference and q-difference with the quaternionic fractional order for the quaternion-valued functions and establish some of their basic properties. Based on this, the summation representations of solutions for the nonlinear quaternion-valued fractional difference equation and q-difference equation are obtained. In addition, several examples are provided to illustrate the feasibility of our obtained results in each section.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2024-0015 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 271 - 304

Submitted on: Feb 9, 2023

Accepted on: May 31, 2023

Published on: May 27, 2024

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Fractional summation,

Quaternion-valued functions,

Quaternionic fractional order,

Quaternion Fractional Difference equations

Related subjects:

Mathematics,

General mathematics

© 2024 Chao Wang, Weiyu Xie, Ravi P. Agarwal, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 32 (2024): Issue 1 (April 2024)