Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems

	Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
Computational Methods for Differential Equations
مقاله 1، دوره 4، شماره 2، تیر 2016، صفحه 99-115 اصل مقاله (1.04 M)
نوع مقاله: Research Paper
نویسندگان
Elmira Ashpazzadeh؛ Mehrdad Lakestani^*
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
چکیده
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.
کلیدواژه‌ها
Caputo fractional derivative؛ Fractional order optimal control؛ Biorthogonal cubic Hermite spline multiwavelets

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