In this report, based on the Caputo definition of fractional derivatives we will obtain the Euler–Lagrange equations for two classes of the generalization of delay fractional variational problems depending on indefinite integrals (DFVPIs). On the other hand, we consider the problems with isoperimetric and holonomic constraints. The direct Rayleigh–Ritz method is applied for solving DFVPIs for the first time. In the present method, the Legendre multiwavelet functions with support of Rayleigh–Ritz have been used to give the best approximate solution for the problem.
