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Spectral collocation method for nonlinear Riemann–Liouville fractional differential system

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Abstract

The spectral collocation method is investigated for the system of nonlinear Riemann–Liouville fractional differential equations (FDEs). The main idea of the presented method is to solve the corresponding system of nonlinear weakly singular Volterra integral equations obtained from the system of FDEs. In order to carry out convergence analysis for the presented method, we investigate the regularity of the solution to the system of FDEs. The provided convergence analysis result shows that the presented method has spectral convergence. Theoretical results are confirmed by numerical experiments. The presented method is applied to solve multi-term nonlinear Riemann–Liouville fractional differential equations and multi-term nonlinear Riemann–Liouville fractional integro-differential equations.

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Authors and Affiliations

  1. School of Financial Mathematics and Statistic, Guangdong University of Finance, Guangzhou, 510521, China

    Zhendong Gu

  2. School of Accounting, Guangdong University of Finance and Economics, Guangzhou, 510320, China

    Yinying Kong

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  1. Zhendong Gu
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  2. Yinying Kong
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Correspondence to Yinying Kong.

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Z. Gu was supported by Guangdong Natural Science Foundation (2018A030313236), and National Natural Science Foundation of China (11971123); Y. Kong was supported by Guangdong Natural Science Foundation (2018A030313954), Guangdong University (New Generation Information Technology) Key Field Project (2020ZDZX3019), and Project of Guangdong Province Innovative Team (2020WCXTD011).

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Gu, Z., Kong, Y. Spectral collocation method for nonlinear Riemann–Liouville fractional differential system. Calcolo 58, 12 (2021). https://doi.org/10.1007/s10092-021-00403-y

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