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Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations

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Abstract

In this work, we extend the Jacobi spectral approximation to the boundary value problems of nonlinear fractional pantograph differential equations. First, the differential equation is equivalently restated as a Volterra-Fredholm integral equation. Second, we introduce the existence and uniqueness of the solution for the problem. Then, the Jacobi-Gauss points and the Jacobi-Gauss quadrature formula are used to solve the obtained integral equation. The error estimates for the proposed scheme are investigated under the \(L^{\infty }\) norm and the weighted L2 norm. Finally, two illustrative examples are included to confirm our analysis.

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Acknowledgments

The author is very grateful to the reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper.

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  1. Department of Science, Jiangsu Ocean University, Lianyungang, 222005, Jiangsu, China

    Changqing Yang & Jianhua Hou

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  1. Changqing Yang
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  2. Jianhua Hou
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Correspondence to Changqing Yang.

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Yang, C., Hou, J. Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations. Numer Algor 86, 1089–1108 (2021). https://doi.org/10.1007/s11075-020-00924-7

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