A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems

• Main Author: Iman Malmir
• Format: Article
• Language: English
• Published: MDPI AG 2019-09-01
• Series: Fractal and Fractional
• Subjects: fractional integration operational matrix of Chebyshev wavelets; Chebyshev wavelets method; fractional time-delay optimal control; multifractional delay differential equation; quadratically constrained linear-quadratic optimal control; piecewise delay
• Online Access: https://www.mdpi.com/2504-3110/3/3/46
• ISSN: 2504-3110

Fractional integration operational matrix of Chebyshev wavelets based on the Riemann−Liouville fractional integral operator is derived directly from Chebyshev wavelets for the first time. The formulation is accurate and can be applied for fractional orders or an integer order. Using the fractional integration operational matrix, new Chebyshev wavelet methods for finding solutions of linear-quadratic optimal control problems and analysis of linear fractional time-delay systems are presented. Different numerical examples are solved to show the accuracy and applicability of the new Chebyshev wavelet methods.