In present study, we investigate the existence of solution for a multi-term fractional integrodierential system with special boundary conditions under some dierent conditions. In this way, we provide
dierent results for the existence of solutions for the system and also for obtaining unique solution for the
system under dierent conditions. We also present three numerical examples in which by using the Legendre
multi-wavelet method, we approximate solutions of the system. These examples illustrate our main results.