Numerical study of a class of variable order nonlinear fractional differential equation in terms of Bernstein polynomials

In this paper, we use Bernstein polynomials to seek the numerical solution of a class of nonlinear variable order fractional differential equation. The fractional derivative is described in the Caputo sense. Three different kinds of operational matrixes with Bernstein polynomials are derived and are utilized to transform the initial equation into the products of several dependent matrixes which can also be regarded as the system of nonlinear equations after dispersing the variable. By solving the system of equations, the numerical solutions are acquired. Numerical examples are provided to show that the method is computationally efficient and accurate. Keywords: Bernstein polynomials, Variable order fractional nonlinear differential equation, Operational matrix, Numerical solution, Convergence analysis, The absolute erro