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Generalized fractional-order Legendre wavelet method for two dimensional distributed order fractional optimal control problem.
- Source :
-
Journal of Vibration & Control . Apr2024, Vol. 30 Issue 7/8, p1690-1705. 16p. - Publication Year :
- 2024
-
Abstract
- This paper is concerned with a two-dimensional fractional optimal control problem whose governing equations are distributed order fractional differential equations in the Caputo sense. A generalized fractional-order Legendre wavelet method has been used to solve the two-dimensional distributed-order fractional optimal control problem. An exact formula for the Riemann–Liouville integration of generalized fractional-order Legendre wavelet has been derived by using regularized beta functions. This formula and the two-dimensional Gauss–Legendre integration formula have been used to solve the two-dimensional distributed order fractional optimal control problem. Moreover, an L 2-error estimate in the approximation of an unknown function with a generalized fractional-order Legendre wavelet has been derived and the estimated order has been verified for a given function. Furthermore, convergence analysis for the proposed method has been presented. In the last, two test problems have been considered to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10775463
- Volume :
- 30
- Issue :
- 7/8
- Database :
- Academic Search Index
- Journal :
- Journal of Vibration & Control
- Publication Type :
- Academic Journal
- Accession number :
- 176331347
- Full Text :
- https://doi.org/10.1177/10775463231169317