Fractional-order Bernstein wavelets for solving stochastic fractional integro-differential equations

In this study, we construct the fractional-order Bernstein wavelets for solving stochastic fractional integro-differential equations. Fractional-order Bernstein wavelets and their properties are presented for the first time.  The fractional integral operator of fractional-order Bernstein wavelets together with the Gaussian integration method is applied to reduce stochastic fractional integro-differential equations to the solution of algebraic equations which can be simply solved to obtain the solution of the problem.  Also, an error estimation for our approach is introduced.  The numerical results demonstrate that our scheme is simply applicable, efficient, powerful and very precise at the small number of basis functions.