Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.22/6963
Título: A Review of Operational Matrices and Spectral Techniques for Fractional Calculus
Autor: Bhrawy, A. H.
Taha, T. M.
Machado, J. A. Tenreiro
Palavras-chave: Multi-term FDEs
Operational matrices
Legendre polynomials
Jacobi polynomials
Chebyshev polynomials
Bernstein polynomials
Generalized Laguerre polynomials
Modified generalized Laguerre polynomials
Tau method
Collocation method
Data: 2015
Editora: Springer
Relatório da Série N.º: Nonlinear Dynamics;Vol. 81, Issue 3
Resumo: Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.
URI: http://hdl.handle.net/10400.22/6963
DOI: 10.1007/s11071-015-2087-0
Versão do Editor: http://link.springer.com/article/10.1007/s11071-015-2087-0
Aparece nas colecções:ISEP - DEE - Artigos

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