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On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay
Author(s) -
Dehestani Haniye,
Ordokhani Yadollah,
Razzaghi Mohsen
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2259
Subject(s) - mathematics , wavelet , collocation method , matrix (chemical analysis) , fractional calculus , mathematical analysis , collocation (remote sensing) , algebraic equation , differential equation , nonlinear system , computer science , ordinary differential equation , materials science , physics , quantum mechanics , artificial intelligence , machine learning , composite material
Summary A novel collocation method based on Genocchi wavelet is presented for the numerical solution of fractional differential equations and time‐fractional partial differential equations with delay. In this work, to achieve the approximate solution with height accuracy, we employed the operational matrix of integer derivative and the pseudo‐operational matrix of fractional derivative in Caputo sense. Also, based on Genocchi function properties, we presented delay and pantograph operational matrices of Genocchi wavelet functions (GWFs). Due to operational and pseudo‐operational matrices, the equations under this study can be turned into nonlinear algebraic equations with the unknown GWF coefficients. For illustrating the upper bound of error for the proposed method, we estimate the error in the sense of Sobolev space. In addition, to demonstrate the efficacy of the pseudo‐operational matrix of fractional derivative, we investigate the upper bound of error for the mentioned matrix. Finally, the algorithm based on the proposed approach is implemented for some numerical experiments to confirm accuracy and applicability.