Utilizing General Lagrange Scaling Functions for Two Classes of Fractional Optimal Control Problems
نویسندگان
1 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
2 Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran
3 Faculty of Science, Mahallat Institute of Higher Education, Mahallat, Iran
doi
10.22052/ijmc.2025.257438.2053چکیده
This manuscript examines two categories of fractional optimal control problems (FOCPs) with fractional system and delay fractional system constraints. This scheme is based on the general Lagrange scaling functions (GLSFs), which can generate both orthogonal and non-orthogonal scaling functions by selecting different Lagrange nodes. Notably, the method is designed to be applied without initially choosing specific Lagrange nodes; instead, we leverage the potential advantages of GLSFs to develop new methods by considering various Lagrange nodes.Additionally, a general Riemann-Liouville fractional integration operational matrix (GR-LOP) and a general delay operational matrix (GDOP) are proposed for the considered functions. Next, by combining these operational matrices and the Gauss-Legendre integration method, we transform the original problems into systems of algebraic equations. To demonstrate the effectiveness of the proposed GLSF method, five numerical examples are provided.
