Utilizing General Lagrange Scaling Functions for Two Classes‎ ‎of‎ ‎Fractional‎ ‎Optimal‎ ‎Control‎ ‎Problems

Document Type : Research Paper

Authors

1 Department of Mathematics Education‎, ‎Farhangian University‎, ‎P.O‎. ‎Box 14665-889‎, ‎Tehran‎, ‎Iran

2 Department of Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Alzahra University‎, ‎Tehran‎, ‎Iran

3 Faculty of Science‎, ‎Mahallat Institute of Higher Education‎, ‎Mahallat‎, ‎Iran

10.22052/ijmc.2025.257438.2053

Abstract

‎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.

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Main Subjects


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