In this study, a new hybrid method is developed to solve a system of linear or nonlinear fractional differential equations using Bernoulli wavelets (Bws) and the least square support vector regression(LS-SVR). For this purpose, we present Bw operator of Riemann-Liouville fractional integration for Bw and use it in our scheme. In the proposed technique, we approximate the unknown functions via Bws, then with the help of Bw operator of fractional integration and LS-SVR, we reduce the problem to an algebraic system. In this way, we simplify the computation of the considered system. The error analysis is proposed. Finally, we demonstrate the applicability of the present scheme by solving several numerical examples.