Numerical solutions for systems of fractional order differential equations with Bernoulli wavelets

In this paper, an effective algorithm for solving systems of fractional order differential equations (FDEs) is proposed. The algorithm is based on Bernoulli wavelets function approximation, which has never been used for systems of FDEs. The main purpose of this algorithm is to combine Bernoulli wavelets function approximation with its fractional integral operator matrix to transform the studied systems of fractional differential equations into easily solved systems of algebraic equations. Illustrative examples are included to reveal the effectiveness of the algorithm and the accuracy of the convergence analysis.