A highly accurate numerical method for fractional electrohydrodynamic flow equation

In this study, the nonlocal effects in a fractional-order electrohydrodynamic flow model—which characterizes the velocity of an ionized fluid within a circular cylindrical conduit—are examined by employing a smooth composite pseudospectral method to achieve highly accurate numerical solutions. The model adopts the Caputo definition for fractional derivatives and ensures smoothness at the endpoints of each subdomain, setting it apart from traditional finite difference methods. The velocity fields of the electrohydrodynamic flow are analyzed with respect to three key parameters: the strength of nonlinearity, the electrical Hartmann number, and the orders of the fractional derivatives. A comprehensive error analysis is provided, and a comparative evaluation with existing methods in the literature confirms the superior stability and accuracy of the proposed approach. This study contributes to a deeper understanding of nonlocal effects in electrohydrodynamics and enhances the broader application of fractional calculus, paving the way for more precise and reliable computational models in applied sciences.