Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method
Sedigheh Sabermahani, Yadollah Ordokhani
Abstract
A new approach to finding the approximate solution of distributed-order fractional optimal control problems (D-O FOCPs) is proposed. This method is based on Fibonacci wavelets (FWs). We present a new Riemann–Liouville operational matrix for FWs using the hypergeometric function. Using this, an operational matrix of the distributed-order fractional derivative is presented. Implementing the mentioned operational matrix with the help of the Gauss–Legendre numerical integration, the problem converts to a system of algebraic equations. Error analysis is proposed. Finally, the validation of the present technique is checked by solving some numerical examples.
Topics & Concepts
Legendre waveletMathematicsAlgebraic equationApplied mathematicsWaveletFractional calculusMatrix (chemical analysis)Fibonacci numberMathematical optimizationOrder (exchange)Computer scienceWavelet transformDiscrete wavelet transformDiscrete mathematicsMaterials sciencePhysicsQuantum mechanicsEconomicsNonlinear systemArtificial intelligenceComposite materialFinanceFractional Differential Equations SolutionsAdvanced Control Systems DesignNumerical methods for differential equations