Jacobi wavelet operational matrix of fractional integration for solving fractional integro-differential equation

2015 International Conference on Mathematics, its Applications, and Mathematics Education

数学;教育

Rong, Loh Jian^1 ; Chang, Phang^1

Department of Science and Mathematics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Parit Raja, Johor, Batu Pahat

86400, Malaysia^1

关键词: Fractional differential equations;    Fractional integration;    Fractional integro-differential equation;    Jacobi polynomials;    Legendre waveletss;    Operational matrices;    Operational methods;    Orthogonal wavelets;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/693/1/012002/pdf
DOI  :  10.1088/1742-6596/693/1/012002

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

In this paper, we first define generalized shifted Jacobi polynomial on interval and then use it to define Jacobi wavelet. Then, the operational matrix of fractional integration for Jacobi wavelet is being derived to solve fractional differential equation and fractional integro-differential equation. This method can be seen as a generalization of other orthogonal wavelet operational methods, e.g. Legendre wavelets, Chebyshev wavelets of 1st kind, Chebyshev wavelets of 2nd kind, etc. which are special cases of the Jacobi wavelets. We apply our method to a special type of fractional integro-differential equation of Fredholm type.