Fractional‐order Chebyshev wavelet method for variable‐order fractional optimal control problems
Ghodsieh Ghanbari, Mohsen Razzaghi
Abstract
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.
Topics & Concepts
MathematicsWaveletFractional calculusChebyshev filterAlgebraic equationApplied mathematicsChebyshev equationOrder (exchange)Legendre waveletVariable (mathematics)Chebyshev nodesConvergence (economics)Mathematical optimizationMathematical analysisWavelet transformDiscrete wavelet transformOrthogonal polynomialsComputer scienceNonlinear systemArtificial intelligencePhysicsEconomic growthQuantum mechanicsEconomicsFinanceClassical orthogonal polynomialsFractional Differential Equations SolutionsAdvanced Control Systems DesignIterative Methods for Nonlinear Equations