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In this study, we present a new approximation method to give an explicit solution of a laminar flow using a Sisko model. This is a problem of a generalized Newtonian fluid with slip boundary conditions. The proposed method is based on the variational iteration method (VIM) combined with an approximation step. This method is validated where the exact solution is available. In addition, in order to enrich the discussion, a numerical method is presented. The results illustrate that the VIM may be more effective that the finite difference method for a dilatant fluid. However, the VIM will be inappropriate for pseudoplastic fluid cases.

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In this work, we have developed a semi-analytical method, based on the combination of the differential transform method and the Laplace transform, to solve a class of linear and nonlinear differential equations with a proportional delay. In order to provide sufficient precision to meet computational needs, we have resumed some proofs of differential transform properties. Some illustrative and physical examples presented and compared to analytical solutions show promising results regarding the validity and applicability of this approach.

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In this paper, an iterative method is applied to solve some p-Laplacian boundary value problem involving Riemann-Liouville fractional derivative operator. More precisely, we establish the existence of two positive solutions. Moreover, we prove that these solutions are one maximal and the other is minimal. An example is presented to illustrate our main result. Finally, a numerical method to solve this problem is given.