<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we introduce the basic notions of the fractional summation, difference and <italic>q</italic>-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 <italic>q</italic>-difference equation are obtained. In addition, several examples are provided to illustrate the feasibility of our obtained results in each section.</p>
</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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we introduce the basic notions of the fractional summation, difference and q-difference with the quaternionic fractional order for the...

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

Published Online: May 27, 2024

Page range: 271 - 304

Received: Feb 09, 2023

Accepted: May 31, 2023

DOI: https://doi.org/10.2478/auom-2024-0015

Keywords
Fractional summation, Quaternion-valued functions, Quaternionic fractional order, Quaternion Fractional Difference equations

© 2024 Chao Wang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: May 27, 2024

Page range: 271 - 304

Received: Feb 09, 2023

Accepted: May 31, 2023

DOI: https://doi.org/10.2478/auom-2024-0015

KeywordsFractional summation, Quaternion-valued functions, Quaternionic fractional order, Quaternion Fractional Difference equations

© 2024 Chao Wang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Fractional summation, Quaternion-valued functions, Quaternionic fractional order, Quaternion Fractional Difference equations