Journal of Guangxi Normal University(Natural Science Edition) ›› 2023, Vol. 41 ›› Issue (3): 130-143.doi: 10.16088/j.issn.1001-6600.2022050602

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The Sixth Kind of Chebyshev Wavelet Collocation Method for Numerical Solutions of Fractional Differential Equations

HUANG Yingjie, ZHOU Fengying*, XU Xiaoyong, HE Hongmei   

  1. School of Science, East China University of Technology, Nanchang Jiangxi 330013, China
  • Received:2022-05-06 Revised:2022-07-20 Online:2023-05-25 Published:2023-06-01

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Abstract: Based on the sixth kind of Chebyshev wavelet collocation method, a numerical method for solving fractional differential equations is proposed. By using the shifted sixth kind of Chebyshev polynomials and under the definition of Riemann-Liouville fractional order, the exact expressions of the fractional order integral formulas of the sixth kind of Chebyshev wavelet functions are obtained. Using the integral formulas together with the effective collocation method, the problem of solving fractional differential equations is transformed into algebraic equations. The uniform convergence analysis of the expansion of the sixth kind of Chebyshev wavelet functions and error estimation in the sense of L2 norm are given. Numerical examples show the applicability and effectiveness of the algorithm.

Key words: the sixth kind of Chebyshev wavelet, fractional order differential equation, Riemann-Liouville fractional integration, Caputo fractional differential, collocation method

CLC Number:  O241.8
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