Solution of linear fractional partial differential equations based on the operator matrix of fractional Bernstein polynomials and error correction

International Journal of Innovative Computing and Applications, Inderscience Publishers, 2018, 14, pp.211 - 226

Wenhui Li 1,2, Ling Bai 3, Yiming Chen 3,4,5, Serge Santos 6, Baofeng Li 7

1 School of Information Science and Engineering
2 The Key Laboratory for Special Fiber and Fiber Sensor of Hebei Province
3 College of ScienceYanshan University, No. 438, Hebei Avenue, Qinhuangdao 066004, P. R. China
4 LE STUDIUM - LE STUDIUM Loire Valley Institute for Advanced Studies, 45000 Orléans, France
5 PRISME - Laboratoire pluridisciplinaire de recherche en ingénierie des systèmes, mécanique et énergétique, Bourges, France
6 INSA Centre Val de LoireUniversity of Orleans, PRISME EA 4229, Bourges Cedex 18022, France
7 College of SciencesTangshan Normal University, No. 156, Jianshe North Road, Tangshan 063000, P. R. China


In this paper, firstly, a new method which makes a modification of the Bern-stein polynomials is introduced to solve the linear fractional partial differential equations (FPDEs). The biggest advantage of the fractional Bernstein polynomials is that the order can be changed with the order of the fractional partial differential equations. For the first time, we try to use this method to solve the linear fractional partial differential equations. Secondly, convergence analysis and error correction are also given to make the calculation results more accurate. The concrete content of this method and error correction are explained briefly and numerical examples are given to demonstrate the validity and accuracy of the method.


Fractional Bernstein polynomials
Linear fractional partial differential equation
Operator matrix
Convergence analysis
Error correction
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International Journal of Innovative Computing