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The magnetohydrodynamic (MHD) peristaltic flow of the fractional Jeffrey fluid through porous medium in a nonuniform channel is presented. The fractional calculus is considered in Darcy’s law and the constitutive relationship which included the relaxation and retardation behavior. Under the assumptions of long wavelength and low Reynolds number, the analysis solutions of velocity distribution, pressure gradient, and pressure rise are investigated. The effects of fractional viscoelastic parameters of the generalized Jeffrey fluid on the peristaltic flow and the influence of magnetic field, porous medium, and geometric parameter of the nonuniform channel are presented through graphical illustration. The results of the analogous flow for the generalized second grade fluid, the fractional Maxwell fluid, are also deduced as special cases. The comparison among them is presented graphically.

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SUMMARYBased on Davidson method for solving generalized eigenvalue problems, a new method for synchro calculation of eigenpairs and their partial derivatives of generalized eigenvalue problems is presented. Eigenpairs and their partial derivatives are computed simultaneously. The equation systems that are solved for eigenvector partial derivatives can be greatly reduced from the original matrix sizes, thus the e ciency of computing eigenvector partial derivatives is improved. Numerical results show that the proposed method is e cient, especially for the large-scale symmetric generalized eigenvalue problems.