Vectorial reduced differential transform method for fractional Cauchy–Riemann system of equations

Abstract

Cauchy–Riemann equations are very important as with condition of differentiability and continuity; these are the necessary and sufficient conditions for function to be analytic. Physically, Cauchy–Riemann equations represent the curl and divergence of vector fields. Like classical differential equations, a large class of physical problems are plugging with partial differential equations (PDEs). So PDEs need to be generalizing as fractional PDEs. This study proceeded to involves fractionalization of space and time variables of Cauchy–Riemann system of equations. Vectorial fractional reduced differential transformed method is used to solve inhomogeneous fractional Cauchy–Riemann equation in both space and time variable with analytic Cauchy data. Solutions so obtained are in the form of convergent infinite series. The exact and approximate solutions of model problems are shown graphically and observed that the solutions are in good agreement with exact solution for α = β = 1.