The Laplace-collocation method for solving fractional differential equations and a class of fractional optimal control problems

2018 ◽  
Vol 39 (2) ◽  
pp. 1110-1129 ◽  
Author(s):  
Seyed Ali Rakhshan ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Differential ◽  
Fractional Optimal Control Problems

The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems

2011 ◽  
Vol 17 (13) ◽  
pp. 2059-2065 ◽  
Author(s):  
SA Yousefi ◽  
A Lotfi ◽  
M Dehghan
Keyword(s):  
Optimal Control ◽  
Exact Solution ◽  
Approximate Solution ◽  
Collocation Method ◽  
Algebraic System ◽  
Optimal Control Problems ◽  
New Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

In this article the Legendre multiwavelet basis with the aid of a collocation method has been applied to give the approximate solution for the fractional optimal control problems (FOCPs). The properties of the Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of an algebraic system. Numerical results and a comparison with the exact solution in the cases when we have an exact solution are given to demonstrate the applicability and efficiency of the new method.

Numerical Method for Solving Fractional Optimal Control Problems

2009 ◽  
Author(s):  
Raj Kumar Biswas ◽  
Siddhartha Sen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Control Problems ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Fractional Optimal Control Problems ◽  
The Right

A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Operator is used to convert the right Riemann-Liouville derivative into an equivalent left Riemann-Liouville derivative, and then the two point boundary value problem is solved numerically. The proposed method is straightforward and it uses an available numerical technique to solve fractional differential equations resulting from the formulation. Examples considered here show that the numerical results obtained using this and other techniques agree very well.

Application of Fractional Optimal Control Problems on Some Mathematical Bioscience

2020 ◽  
pp. 41-56
Author(s):  
Ismail Gad Ameen ◽  
Hegagi Mohamed Ali
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Short Review ◽  
Decision Makers ◽  
Fractional Optimal Control ◽  
Fractional Models ◽  
Fractional Differential ◽  
Fractional Optimal Control Problems

In this chapter, the authors present a short review of a fractional-order control models, which are described by a system of fractional differential equations. Fractional derivatives describe the behaviour of dynamical systems better than classical calculus, where it can reflect the effect of memory. This survey shows the effect of the control on the fractional models, which represents epidemiological and biomedicine problems. So, the solution to such models is necessary for decision makers in health organizations.

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