This paper obtains the necessary optimality conditions for a new class of isoperimetric frac- tional variational problems depending on indefinite integrals (IFVPDI). A new condition is added to the IFVPDI and a modified direct numerical approach based on the Epsilon–Ritz method and polynomial basis functions is applied. The optimization problem is reduced to the problem of optimizing a real value function. The convergence and error analysis of the proposed approach are also assessed. Illustrative examples are included demonstrating the validity and applicability of the method.
