Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Abstract
In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville integration and multiplication are then utilized to reduce the given optimization problem to the system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain algebraic equations. Illustrative examples are provided to confirm the applicability of the new method.
Ashpazzadeh, E., & Lakestani, M. (2016). Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems. Computational Methods for Differential Equations, 4(2), 99-115.
MLA
Elmira Ashpazzadeh; Mehrdad Lakestani. "Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems". Computational Methods for Differential Equations, 4, 2, 2016, 99-115.
HARVARD
Ashpazzadeh, E., Lakestani, M. (2016). 'Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems', Computational Methods for Differential Equations, 4(2), pp. 99-115.
VANCOUVER
Ashpazzadeh, E., Lakestani, M. Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems. Computational Methods for Differential Equations, 2016; 4(2): 99-115.
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