Transmutation operator for a radial Vekua equation in quaternion analysis

The theory of the Vekua equation in complex analysis has been extended to higher dimensions with significant applications in mathematical physics. In quaternion and Clifford analysis, solutions of the Vekua equations are commonly represented using Cauchy integrals and Taylor series. Additionally, transmutation operators serve as a powerful tool for constructing these solutions. In this paper, we introduce a radial Vekua equation in quaternion analysis $Du=q\left(r\right)u$, where $r=\left|x\right|$ and $q\left(r\right)=\sum _{i=0}^{+\infty }{a}_i{r}^i$, with $a_i\in R$. We employ a newly modified normalized system of functions with respect to the Dirac operator D to represent its solutions via a transmutation operator using monogenic functions.