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

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.