A generalized fractional-order Chebyshev wavelet method for two-dimensional distributed-order fractional differential equations

•Two-dimensional distributed-order fractional differential equations (DOFDE) are used in different applications.•Recently, the Riemann-Liouville fractional integral operator (RLFIO) of wavelets was not calculated exactly.•We introduce fractional-order Chebyshev wavelets (FOCW) and use them to solve...

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Vydané v:Communications in nonlinear science & numerical simulation Ročník 95; s. 105597
Hlavní autori: Do, Quan H., Ngo, Hoa T.B., Razzaghi, Mohsen
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.04.2021
Elsevier Science Ltd
Predmet:
2-dimensional distributed-order
Chebyshev approximation
Chebyshev wavelet
Differential equations
Formulas (mathematics)
Fractional calculus
Fractional differential equation
Fractions
Operators (mathematics)
Regularized beta function
Wavelet analysis
Wavelet transforms
Fractional differential equation
Chebyshev wavelet
2-dimensional distributed-order
Regularized beta function
ISSN:1007-5704, 1878-7274
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Popis
Shrnutí:•Two-dimensional distributed-order fractional differential equations (DOFDE) are used in different applications.•Recently, the Riemann-Liouville fractional integral operator (RLFIO) of wavelets was not calculated exactly.•We introduce fractional-order Chebyshev wavelets (FOCW) and use them to solve two-dimensional DOFDE.•By applying regularized beta functions we obtain an exact formula for the RLFIO for FOCW.•By using FOCW and the exact formula, we obtain a very effcient and accurate numerical solutions for two-dimensional DOFDE. We provide a new effective method for the two-dimensional distributed-order fractional differential equations (DOFDEs). The technique is based on fractional-order Chebyshev wavelets. An exact formula involving regularized beta functions for determining the Riemann-Liouville fractional integral operator of these wavelets is given. The given wavelets and this formula are utilized to find the solutions of the given two-dimensional DOFDEs. The method gives very accurate results. The given numerical examples support this claim.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2020.105597