Duality for second order nondifferentiable multiobjective fractional variational problems

In the present work, we construct a second order symmetric dual pair with multiobjective and nondifferentiable settings over variational problems and explore weak, strong, and converse duality theorems with the help of second order (F, ?, ?, d)-convexity. First, a parametric method is used to transform the problem into an equivalent non-fractional form. In order to determine the bound on the optimal value of the primal problem and build the theoretical framework for strong duality, we then deduce the weak duality theorem for the designed problems. The strong duality demonstrated in the paper shows that a symmetric relationship exists between the primal and dual problems. The static case is additionally addressed by dropping the time component. The solutions in our work may be applied to a broader class of problems that arise in modeling mechanical engineering problems. The existence of the problem as required in the discussion is demonstrated by constructed examples.