<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

Data publikacji: 27 maj 2024

Zakres stron: 271 - 304

Otrzymano: 09 lut 2023

Przyjęty: 31 maj 2023

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

Słowa kluczowe
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

Data publikacji: 27 maj 2024

Zakres stron: 271 - 304

Otrzymano: 09 lut 2023

Przyjęty: 31 maj 2023

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

Słowa kluczoweFractional 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.

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