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In this paper, we solve a class of fractional   variational   problems (  FVPs  ) by using operational matrix of fractional integration which derived from second order spline (B-spline) basis function. The fractional derivative is defined in the   Caputo   and Riemann-  Liouville   fractional integral operator. The B-spline function with unknown coefficients and B-spline operational matrix of integration are used to replace the fractional derivative which is in the performance index. Next, we applied the method of constrained   extremum   which involved a set of Lagrange multipliers. As a result, we get a system of algebraic equations which can be solve easily. Hence, the value for unknown coefficients of B-spline function is obtained as well as the solution for the   FVPs  . Finally, the illustrative examples shown the validity and applicability of this method to solve   FVPs  .

Numerical Solution for A Class of Fractional Variational Problem via Second Order B-Spline Function