A regularity of split-biquaternionic-valued functions in Clifford analysis

Abstract

We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables.

Expansion of implicit mapping theory to split-quaternionic maps in Clifford analysis

“…We have previously investigated the corresponding Cauchy-Riemann systems and the regularity properties of a split-quaternion-valued function on a split-quaternionic variable [11][12][13]. Kilbas et al [10] provided the most developments on the calculus of integrals and derivatives of any arbitrary real or complex order and fractional differential equations involving many different potentially useful operators of fractional calculus and its applications (see [22]).…”