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Theoretical and spectral numerical study for fractional Van der Pol equation

This manuscript concerns with both theoretical and numerical study for a generalized form of fractional Van der Pol equations (FVDPEs). The Schauder fixed point and Banach contraction mapping principles are used for investigating the existence and uniqueness of the considered problem. The second novelty of this manuscript is using the tau method for solving a nonlinear problem (specially FVDPE). The convergence analysis of the suggested approach is also studied. Comparisons with other numerical approaches are introduced for testing the applicability of the current approach.