The main aim of this thesis is to present a numerical method based on Bernoulli wavelet basis functions for solving a class of fractional order integro-differential equations with weakly singular kernel. To this aim, we will introduce the Riemann–Liouville integral operator of the basis functions and use them to reduce the main problem to a system of algebraic equations. Finally, some examples are included and solved by the proposed scheme and the results show the efficiency and high accuracy of our new technique.
