Using Mott polynomials operational matrices to optimize multi-dimensional fractional optimal control problems

Iranian Journal of Numerical Analysis and Optimization

دوره 12، شماره 1 - شماره پیاپی 21، خرداد 2022، صفحه 201-227   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.68926.1016

نویسندگان

S.A. Alavi^{* 1}؛ A. Haghighi²؛ A. Yari³؛ F. Soltanian³

¹Department of Mathematics,Payame Noor University, Tehran, Iran.

²Department of Mathematics, Technical and Vocational University, Tehran, Iran.

³Department of Mathematics, Payame Noor University, PO BOX 9395-3697, Tehran, Iran.

چکیده

We offer a method for solving the fractional optimal control problems of multi-dimensional. We obtain a fractional derivative and multiplication operational matrix for Mott polynomials (M-polynomials). In the proposed method, the Caputo sense of the fractional derivative is applied on dynamical system. The main feature of this method is to reduce the problem into a system of algebraic equations in order to simplify it. We also show that by increasing the approximation points, the responses converge to the real answer. When the degree of fractional derivative approaches to 1, then the obtained solution approaches to the classical solution as well.

کلیدواژه‌ها

Mott polynomials؛ Caputo derivative؛ fractional optimal control problems؛ operational matrix

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