On some classes of functions of the reduced quaternionic variable and their applications in continuum mechanics

In 1992 Professor Leutwiler from the University of Erlangen got a new class of functions of the reduced quaternionic variable as the class of solutions of new generalization of the Cauchy-Riemann system with varying coefficients in $R^3$. In 2003 the author constructed a new axial-symmetric generalization of the Cauchy-Riemann system in $R^3$. During a recent conference in Greece ICNAAM 2011 their applications for some problems of mechanics in inhomogeneous continuous media were demonstrated.