scholarly journals Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
O. M. Saad ◽  
D. G. Mohamed
Keyword(s):  
Optimal Control ◽  
West Nile Virus ◽  
Time Delay ◽  
Numerical Approach ◽  
Transmission Dynamics ◽  
West Nile ◽  
Fractional Optimal Control ◽  
Control Time ◽  
Virus Model ◽  
And Control

Backward Bifurcation and Optimal Control in Transmission Dynamics of West Nile Virus

2010 ◽  
Vol 72 (4) ◽  
pp. 1006-1028 ◽  
Author(s):  
Kbenesh W. Blayneh ◽  
Abba B. Gumel ◽  
Suzanne Lenhart ◽  
Tim Clayton
Keyword(s):  
Optimal Control ◽  
West Nile Virus ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
West Nile

Implementation of fractional optimal control problems in real-world applications

2020 ◽  
Vol 23 (6) ◽  
pp. 1783-1796
Author(s):  
Neelam Singha
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Order Model ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Real World Applications ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order model describes the interaction of effector-immune cells and tumor cells, including combined chemo-immunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractional-order optimal control problem. The key motive is to perform numerical simulations that shall facilitate us in understanding the behavior of state and control variables. Further, the graphical interpretation of solutions effectively validates the applicability of the present analysis to investigate the growth of cancer cells in the presence of medical treatment.

Traveling Waves and Spread Rates for a West Nile Virus Model

2006 ◽  
Vol 68 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Mark Lewis ◽  
Joanna Rencławowicz ◽  
P. van den Driessche
Keyword(s):  
West Nile Virus ◽  
Traveling Waves ◽  
West Nile ◽  
Virus Model

An efficient approximate method for solving two-dimensional fractional optimal control problems using generalized fractional order of Bernstein functions

2020 ◽  
Author(s):  
Ali Ketabdari ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Operational Matrix ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Control Variables ◽  
Fractional Optimal Control ◽  
Bernstein Functions ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract We define a new operational matrix of fractional derivative in the Caputo type and apply a spectral method to solve a two-dimensional fractional optimal control problem (2D-FOCP). To acquire this aim, first we expand the state and control variables based on the fractional order of Bernstein functions. Then we reduce the constraints of 2D-FOCP to a system of algebraic equations through the operational matrix. Now, one can solve straightforward the problem and drive the approximate solution of state and control variables. The convergence of the method in approximating the 2D-FOCP is proved. We demonstrate the efficiency and superiority of the method by comparing the results obtained by the presented method with the results of previous methods in some examples.

The approximate solution of non-linear time-delay fractional optimal control problems by embedding process

2018 ◽  
Vol 36 (3) ◽  
pp. 713-727 ◽  
Author(s):  
E Ziaei ◽  
M H Farahi
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Fractional Derivative ◽  
Optimal Control Problems ◽  
Linear Time ◽  
Control Problems ◽  
Linear Dynamical Systems ◽  
Fractional Optimal Control ◽  
Non Linear ◽  
Fractional Optimal Control Problems

Abstract In this paper, a class of time-delay fractional optimal control problems (TDFOCPs) is studied. Delays may appear in state or control (or both) functions. By an embedding process and using conformable fractional derivative as a new definition of fractional derivative and integral, the class of admissible pair (state, control) is replaced by a class of positive Radon measures. The optimization problem found in measure space is then approximated by a linear programming problem (LPP). The optimal measure which is representing optimal pair is approximated by the solution of a LPP. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to non-linear TDFOCPs. The usefulness of the used idea in this paper is that the method is not iterative, quite straightforward and can be applied to non-linear dynamical systems.

Experimental results of a control time delay system using optimal control

2011 ◽  
Vol 33 (1) ◽  
pp. 100-113 ◽  
Author(s):  
Omar Santos ◽  
Liliam Rodríguez-Guerrero ◽  
Omar López-Ortega
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Delay System ◽  
Experimental Results ◽  
Time Delay System ◽  
Control Time
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