Solving fractional partial differential equations by an efficient new basis

In this paper, we obtain the numerical solution of the general fractional partial differential equations. To this end, we introduce an efficient new basis based on the generalized fractional-order Bernstein functions. A general formulation for the fractional Bernstein operational matrix of fractional integral operator and derivatives operator for the first time is obtained. In this approach, a truncated fractional Bernstein series together with the fractional Bernstein operational matrix are used to reduce the such problems to those of solving a system of algebraic equations thus greatly simplifying the problem. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. Presented results show that the method will improve the solutions of fractional partial differential equations.