Monodiffric differential equations and K-th roots of monodiffric functions

Abstract

A quotient field of monodiffric functions in the first quadrant is set up. With the aid of the elements of this field, called operators, monodiffric differential forms are converted into algebraic forms. The result is a solution to ordinary monodiffric differential equations by operators. Laplace transforms of monodiffric functions are introduced and developed and the concept of Fourier transform is defined. Laplace transforms not only provide a method for solving monodiffric differential equations, but also can be used for extension of a monodiffric function to the whole plane. A direct method analogous to that of continuous theory for solving monodiffric differential equations is developed. The theory of k-th roots of a monodiffric function on the whole complex plane is introduced and regions of existence of the k-th roots of any monodiffric function are given.