A family of fractional analytic polynomials in generalized complex numbers and applications

Abstract

We present the development of fractional generalized complex calculus in the Riemann-Liouville sense, modifying the Cauchy-Riemann operator using the one-dimensional Riemann-Liouville derivative. We analyze the properties of the correspondent fractional analytic functions and introduce a family of analytic polynomials which are necessary to construct series expansions. We provide examples and visuals of these polynomials and use them to solve fractional differential equations and verify fractional Leibniz rule numerically.