Analytic solution of nonlinear singular BVP with multi-order fractional derivatives in electrohydrodynamic flows

Abstract

In this study, a power series formula is proposed in order to introduce a new innovated numerical method called a newly Power Series Method (NPSM), beside with a construction of its error bound, to obtain approximate solutions of the standard fractional counterpart for a Boundary Value Problem (BVP) that appears in ElectroHydroDynamic (EHD) flows of the fluid. The solution for numerous fractional derivatives of both rational and irrational orders are numerically computed. Based on the residual error computation, the validity of the obtained results is verified. A high accuracy and a clear efficiency of the proposed method are revealed by discussing several numerical comparisons between such method and others.