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Theoretical and spectral numerical study for fractional Van der Pol equation
Author(s) -
EzzEldien Samer S.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5666
Subject(s) - mathematics , uniqueness , van der pol oscillator , novelty , numerical analysis , fractional calculus , convergence (economics) , nonlinear system , contraction (grammar) , mathematical analysis , medicine , philosophy , physics , theology , quantum mechanics , economics , economic growth
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.