In the sequel, the numerical solution of a new class of nonlinear optimal control problems (OCPs) generated by Atangana-Baleanu-Caputo (ABC) variable order (V-O) fractional derivative (FD) and fractional Volterra-Fredholm integro-differential equations (FVFIDEs) is found by Bezier curve method (BCM). The main idea behind this work is the use of the BCM. In this technique, the solution is found in the form of a rapid convergent series. Using this method, it is possible to obtain BCM solution of the general form of multipoint boundary value problems. To shown the efficiency of the developed method, numerical results are stated as the main results in this study.