Necessary and Sufficient Criteria of Efficiency in Fractional Multiple Cost Extremization Models

Abstract This paper investigates necessary and sufficient criteria of efficiency in fractional multiple cost constrained extremization models governed by Riemann–Liouville fractional-type integrals and dynamical systems represented through partial differential equations. Using generalized convexities for the considered functionals, the study extends traditional variational principles to fractional multiple cost constrained extremization models involving Riemann–Liouville fractional-type integrals, ensuring the identification of Pareto-type solutions. Additionally, the paper develops robust analytical techniques to address challenges determined by multi-dimensional domains and coupled dynamical systems.