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 D u = q ( r ) u , where r = | x | and q ( r ) = ∑ i = 0 + ∞ a i r i , with a i ∈ 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. • A new radial Vekua's equation in quaternion analysis. • A new modified normalized system of functions with respect to the Dirac operator. • Explicit integral kernels of the transmutation operator.