Akademik Veri Yönetim Sistemi
Results in Control and Optimization, cilt.23, 2026 (ESCI, Scopus)
This work introduces and investigates two- and three-dimensional optimal control problems formulated using the ψ-tempered fractional derivative. The solution approach is constructed by employing the α-Morgan–Voyce together with (α,ψ)-Morgan–Voyce functions as the chosen basis functions. The (α,ψ)-Morgan–Voyce functions are constructed and their properties are presented. To facilitate the practical use of these functions, we construct a set of integral operators corresponding to their integer-order and ψ-tempered fractional-order integrals. The problem under investigation is reformulated into equivalent variational form. By approximating the state variable and its derivatives through the proposed basis functions and the associated integral operators, and subsequently applying the Gauss–Legendre numerical integration, the original formulation is transformed into a system of algebraic equations. Finally, the convergence of the proposed method is thoroughly analyzed, and three numerical examples are provided to illustrate the reliability and practical applicability of the developed technique.