Conditional Optimization Problems: Fractional Order Case

In this manuscript, we introduce a new formulation for the constrained optimization problems in which the objective function is considered in the fractional integral form. The constraints are applied in two separate cases, namely, fractional differential and fractional isoperimetric constraints. In both cases, by using the extended Euler–Lagrange equations and the Lagrange multiplier method, the necessary conditions are obtained. An example is given in order to illustrate the effectiveness of the reported results.