ANALYTIC SOLUTION OF NONLINEAR SINGULAR BVP WITH MULTI-ORDER FRACTIONAL DERIVATIVES IN ELECTROHYDRODYNAMIC FLOWS

ANALYTIC SOLUTION OF NONLINEAR SINGULAR BVP WITH MULTI-ORDER FRACTIONAL DERIVATIVES IN ELECTROHYDRODYNAMIC FLOWS

R. B. Albadarneh, A. K. Alomari, N. Tahat, I. Batiha

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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 ElectroHy- droDynamic (EHD) ows of the uid. The solution for numerous fractional derivativesof both rational and irrational orders are numerically computed. Based on the residual error computation, the validity of the obtained results is veried. A high accuracy and a clear eciency of the proposed method are revealed by discussing several numerical comparisons between such method and others.

Keywords

ElectroHydroDynamic ow, Caputo's fractional derivative, power series method, Residual error.