A new approximate technique is introducing to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives are replaced by Caputo operator, and the solution is demonstrated by Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW). We demonstrate the convergence analysis for this technique to emphasize its reliability. The applicability of the HOBW is demonstrated using three examples. The approximate results of this technique are compared with the correct solutions, which show that this technique has approval with the correct solutions to the problems.