منیره نصرتی

The aim of this paper is to study the fractional order nonlinear singular boundary value problem arising in electrohydrodynamics flow, which describes the velocity of the ionized fluid in a circular cylindrical conduit. For this purpose, Lucas polynomials are employed via spectral collocation and Galerkin methods for reducing the nonlinear singular differential equation of fractional order to an algebraic nonlinear system, which is solved by Newton iterative method. The problem includes two important parameters, including the nonlinearity and Hartman numbers. The effect of these parameters and the influence of fractional order derivatives on the velocity of the fluid is discussed. Based on the reported results in tables and figures, for large values of Hartman number and the fractional derivatives, as well as weak nonlinearity parameter, the velocity profile was increased. The purposed schemes are simple and attractive, and their accuracy and efficiency, were confirmed by studying some cases of main problem and a comparison of the numerical results with the results obtained by some other methods.