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Alavi, Seyyed Ali, Haghighi, Ahmadreza, Yari, Ayatollah, Soltanian, Fahimeh. (1401). A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials. سامانه مدیریت نشریات علمی, 10(3), 755-773. doi: 10.22034/cmde.2021.39419.1728
Seyyed Ali Alavi; Ahmadreza Haghighi; Ayatollah Yari; Fahimeh Soltanian. "A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials". سامانه مدیریت نشریات علمی, 10, 3, 1401, 755-773. doi: 10.22034/cmde.2021.39419.1728
Alavi, Seyyed Ali, Haghighi, Ahmadreza, Yari, Ayatollah, Soltanian, Fahimeh. (1401). 'A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials', سامانه مدیریت نشریات علمی, 10(3), pp. 755-773. doi: 10.22034/cmde.2021.39419.1728
Alavi, Seyyed Ali, Haghighi, Ahmadreza, Yari, Ayatollah, Soltanian, Fahimeh. A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials. سامانه مدیریت نشریات علمی, 1401; 10(3): 755-773. doi: 10.22034/cmde.2021.39419.1728

A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials

Computational Methods for Differential Equations
مقاله 15، دوره 10، شماره 3، مهر 2022، صفحه 755-773    اصل مقاله (487.59 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39419.1728
نویسندگان
Seyyed Ali Alavi1؛ Ahmadreza Haghighi2؛ Ayatollah Yari* 3؛ Fahimeh 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 19395-3697, Tehran, Iran.
چکیده
This paper presents a numerical method for solving a class of fractional optimal control problems (FOCPs) based on numerical polynomial approximation. The fractional derivative in the dynamic system is described in the Caputo sense. We used the approach to approximate the state and control functions by the Mott polynomials (M-polynomials). We introduced the operational matrix of fractional Riemann-Liouville integration and apply it to approximate the fractional derivative of the basis. We investigated the convergence of the new method and some examples are included to demonstrate the validity and applicability of the proposed method.
کلیدواژه‌ها
Fractional optimal control problem؛ Caputo derivative؛ Mott polynomials basis؛ Operational matrix
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