A Fractional Calculus Approach to Interval-Valued Variational Programming Problems

This study explores a class of fractional interval-valued variational programming problems involving the Caputo-Fabrizio (C-F) fractional derivative. By employing the concepts of invex and generalized invex functions, we establish sufficient optimality conditions for these problems. Additionally, we develop a Wolfe-type dual formulation and investigate the corresponding dualityrelationships. In particular, we derive and prove the weak, strong, and converse duality theorems to establish a connection between the primal and dual problems. The theoretical findings are further illustrated through carefully constructed numerical examples, demonstrating the applicability and effectiveness of the proposed approach.