Weak Sharpness and Minimum Principle Sufficiency in Variational Inequalities with Fractional Curvilinear Integral Functional Constraints

Résumé

This paper develops a comprehensive theoretical framework for analyzing weak sharp solutions and minimum principle sufficiency conditions in variational inequalities with fractional curvilinear integral functional constraints. By extending classical variational analysis to the fractional calculus setting, we establish novel characterizations of solution sets through dual gap functionals and geometric properties of feasible regions. We introduce enhanced sufficiency conditions that bridge the gap between convexity assumptions and weak sharpness, providing refined estimates for the distance between arbitrary feasible points and the solution set. The main contributions include: (i) generalized dual gap analysis with explicit modulus of weak sharpness; (ii) equivalence results connecting minimum principle sufficiency to geometric properties of normal and tangent cones; (iii) stability analysis of solution sets under perturbations of the integral kernel; (iv) neutrosophic extension incorporating indeterminacy components for uncertain systems; (v) comprehensive discussion of theoretical and practical implications.