# On the numerical solution of fractional differential equations with cubic nonlinearity via matching polynomial of complete graph

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## Abstract

This study deals with a generalized form of fractional differential equations with cubic nonlinearity, employing a matrix-collocation method dependent on the matching polynomial of complete graph. The method presents a simple and efficient algorithmic infrastructure, which contains a unified matrix expansion of fractional-order derivatives and a general matrix relation for cubic nonlinearity. The method also performs a sustainable approximation for high value of computation limit, thanks to the inclusion of the matching polynomial in matrix system. Using the residual function, the convergence and error estimation are investigated via the second mean value theorem having a weight function. In comparison with the existing results, highly accurate results are obtained. Moreover, the oscillatory solutions of some model problems arising in several applied sciences are simulated. It is verified that the proposed method is reliable, efficient and productive.

## Keywords

Fractional differential equations matrix-collocation method convergence analysis Laplace–Padé method## Notes

### Acknowledgements

The authors would like to thank the reviewers for their constructive and valuable comments to improve the paper.

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