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Wavelet Methods for Solving Fractional-Order Dynamical Systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Wavelet Methods for Solving Fractional-Order Dynamical Systems./
Author:	Rabiei, Kobra.
Description:	1 online resource (112 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
Contained By:	Dissertations Abstracts International83-12B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29066550click for full text (PQDT)
ISBN:	9798438791805

Wavelet Methods for Solving Fractional-Order Dynamical Systems.
Rabiei, Kobra.

Wavelet Methods for Solving Fractional-Order Dynamical Systems. - 1 online resource (112 pages)

Source: Dissertations Abstracts International, Volume: 83-12, Section: B.

Thesis (Ph.D.)--Mississippi State University, 2022.

Includes bibliographical references

In this dissertation, we focus on fractional-order dynamical systems and classify these problems as optimal control of system described by fractional derivative, fractional-order nonlinear differential equations, optimal control of systems described by variable-order differential equations, and delay fractional optimal control problems. These problems are solved by using the spectral method and reducing the problem to a system of algebraic equations. In fact for the optimal control problems described by fractional and variable-order equations, the variables are approximated by chosen wavelets with unknown coefficients in the constraint equations, performance index, and conditions. Thus, a fractional optimal control problem is converted to an optimization problem, which can be solved numerically. We have applied the new generalized wavelets to approximate the fractional-order nonlinear differential equations such as Riccati and Bagley-Torvik equations. Then, the solution to this kind of problem is found using the collocation method. For solving the fractional optimal control described by the fractional delay system, a new set of hybrid functions have been constructed. Also, a general and exact formulation for the fractional-order integral operator of these functions has been achieved. Then we utilized it to solve delay fractional optimal control problems directly. The convergence of the present method is discussed. For all cases, some numerical examples are presented and compared with the existing results, which show the efficiency and accuracy of the present method.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798438791805Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Fractional calculusIndex Terms--Genre/Form:

542853
Electronic books.

Wavelet Methods for Solving Fractional-Order Dynamical Systems.
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500 $a Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
500 $a Advisor: Razzaghi, Mohsen.
502 $a Thesis (Ph.D.)--Mississippi State University, 2022.
504 $a Includes bibliographical references
520 $a In this dissertation, we focus on fractional-order dynamical systems and classify these problems as optimal control of system described by fractional derivative, fractional-order nonlinear differential equations, optimal control of systems described by variable-order differential equations, and delay fractional optimal control problems. These problems are solved by using the spectral method and reducing the problem to a system of algebraic equations. In fact for the optimal control problems described by fractional and variable-order equations, the variables are approximated by chosen wavelets with unknown coefficients in the constraint equations, performance index, and conditions. Thus, a fractional optimal control problem is converted to an optimization problem, which can be solved numerically. We have applied the new generalized wavelets to approximate the fractional-order nonlinear differential equations such as Riccati and Bagley-Torvik equations. Then, the solution to this kind of problem is found using the collocation method. For solving the fractional optimal control described by the fractional delay system, a new set of hybrid functions have been constructed. Also, a general and exact formulation for the fractional-order integral operator of these functions has been achieved. Then we utilized it to solve delay fractional optimal control problems directly. The convergence of the present method is discussed. For all cases, some numerical examples are presented and compared with the existing results, which show the efficiency and accuracy of the present method.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Fractional calculus
653 $a Nonlinear differential equations
653 $a Optimal control problems
653 $a Wavelet methods
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710 2 $a Mississippi State University. $b Mathematics and Statistics. $3 1682213
773 0 $t Dissertations Abstracts International $g 83-12B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29066550 $z click for full text (PQDT)