Bernstein polynomials method for a class of generalized variable order fractional differential equations

This research investigated numerical solutions of generalized variable order fractional partial differential equations by using Bernstein polynomials. In addition, the Caputo differential derivative was adopted. Among fractional operational matrices, which contained x or t, of Bernstein polynomials were derived and utilized to transform the initial equation into the solution of algebraic equations after dispersing the variable. By solving algebraic equations, numerical solutions were acquired. The method, in general, is easy to implement and yields good results. Numerical examples are provided to demonstrate the validity and applicability of the method.