Mathematical Methods in the Applied Sciences · 2021 · 14 citations · 33 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsOptimizationControl TheoryNumerical AlgorithmsNumerical AnalysisNumerical IntegrationNumerical Methods For Differential EquationsOptimal ControlFractional Differential EquationsFractional-order ControlNonlinear Differential-algebraic EquationsNonlinear Function ApproximationWavelet Analysis
A new alternative numerical method for solving variable‐order fractional optimal control problems (VO‐FOCPs) is introduced. We use fractional‐order Chebyshev wavelets for solving these VO‐FOCPs. By applying the regularized beta functions, an exact value for the fractional integration of the given wavelets is provided. By applying this formula and the given wavelets, we reduce the given VO‐FOCP to a system of algebraic equations which can be solved by using known methods. For the function approximation of our method, we also give the convergence analysis. By using several numerical examples, we show that this method is more accurate than the other existing methods in the literature.
33