Abstract
In this study, we mainly discuss the application of the Jacobi collocation method to a class of fractional-order pantograph delay differential equations. We first convert the problem to a nonlinear Volterra integral equation with a weakly singular kernel. Under reasonable assumptions of nonlinearity, the existence and uniqueness of the obtained integral equation are derived. Then, we apply a numerical scheme based on the Jacobi collocation approximation to solve the equivalent integral equation. Furthermore, an error analysis for the numerical scheme is performed. Finally, numerical examples are presented to validate our theoretical analysis.
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Acknowledgements
This research is supported by Nature Science Foundation of Jiangsu (BK20181483). The authors would like to thank the editor and the reviewers for their constructive comments and suggestions for the improvement of the paper.
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Yang , C., Hou, J. & Lv, X. Jacobi spectral collocation method for solving fractional pantograph delay differential equations. Engineering with Computers 38, 1985–1994 (2022). https://doi.org/10.1007/s00366-020-01193-7
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DOI: https://doi.org/10.1007/s00366-020-01193-7
Keywords
- Fractional pantograph differential equation
- Jacobi polynomial
- Collocation method
- Convergence analysis
- Caputo derivative