In this paper, we formulate and prove necessary and sufficient conditions of geodesic efficiency associated with a new class of multiobjective fractional variational control problems governed by geodesic quasiinvex path-independent curvilinear integral functionals and mixed constraints involving first order PDE of m-flow type. Under \( \displaystyle (\rho , b) \)-geodesic quasiinvexity assumptions, by using the new notion of (normal) geodesic efficient solution, we set sufficient conditions of geodesic efficiency for a feasible solution in the considered variational control problems.

中文翻译：

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具有测地准拟曲线积分函数的黎曼流形上的变分控制问题的效率

在本文中，我们制定并证明了与一类新的多目标分数变分控制问题有关的测地效率的必要条件和充分条件，这些问题由与测地准拟路径无关的曲线积分函数和涉及m流一阶PDE的混合约束控制。在\（\ displaystyle（\ rho，b）\）-大地准拟不变性假设下，通过使用（正常）测地有效解的新概念，我们为考虑的变分控制问题中的可行解设定了测地效率的充分条件。