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

Wang, Chao; Xie, Weiyu; Agarwal, Ravi P.

doi:10.2478/auom-2024-0015

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

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