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A numerical method for solving variable‐order fractional diffusion equations using fractional‐order Taylor wavelets
Author(s) -
Vo Thieu N.,
Razzaghi Mohsen,
Toan Phan Thanh
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22761
Subject(s) - mathematics , taylor series , fractional calculus , wavelet , operator (biology) , order (exchange) , variable (mathematics) , collocation (remote sensing) , mathematical analysis , collocation method , differential equation , computer science , ordinary differential equation , biochemistry , chemistry , finance , repressor , artificial intelligence , machine learning , transcription factor , economics , gene
This paper aims to provide a new numerical method for solving variable‐order fractional diffusion equations. The method is constructed using fractional‐order Taylor wavelets. By using the regularized beta function, a formula for computing the exact value of Riemann‐Liouville fractional integral operator of the fractional‐order Taylor wavelets is given. The Taylor wavelets properties and the formula are used in combination with a spectral collocation method to reduce the given diffusion equation to a system of algebraic equations. The method is easy to implement, and gives very accurate solutions. Several examples are given to show the applicability and the effectiveness of the method.