In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effects. The main purpose of the present paper is to develop and analyze a Caputo-Fabrizio fractional derivative model for the HIV/AIDS epidemic which includes an antiretroviral treatment compartment. The existence and uniqueness of the system of solutions of the model are established using a fixed-point theorem and an iterative method. The model is shown to have a disease-free and an endemic equilibrium point. Conditions are derived for the existence of the endemic equilibrium point and for the local asymptotic stability of the disease-free equilibrium point. The results confirm that the disease-free equilibrium point becomes increasingly stable as the fractional order is reduced. Numerical simulations are carried out using a three-step Adams-Bashforth predictor method for a range of fractional orders to illustrate the effects of varying the fractional order and to support the theoretical results.
A class of non-standard optimal control problems is considered. The non-standard feature of these optimal control problems is that they are of neither fixed final time nor of fixed final state. A method of solution is devised which employs a computational algorithm based on control parametrization techniques. The method is applied to the problem of maximizing the range of an aircraft-like gliding projectile with angle of attack control.
In Thailand, the harvesting season for sugarcane usually begins in November and ends the following May. At the beginning of each harvesting season, the Royal Thai government sets the price of two types of sugarcane, namely fresh and fired, based on sweetness (sugar content) and gross weight of sugarcane delivered to the sugar factories. The aim of the present research is to determine optimal harvesting policies for the two types of sugarcane in sugarcane producing regions of Thailand in order to maximize revenue and minimize harvesting cost. In this paper, a harvesting policy is defined as the amount of each type of sugarcane harvested and delivered to the sugar factories during each 15-day period of a harvesting season. Two optimization methods have been used to solve this optimization problem, namely the ε-constraints method and a quasi-Newton optimization method. In the ε-constraints method, the problem is considered as a bi-objective optimization problem with the main objective being to determine harvesting policies that maximize the total revenue subject to upper bounds on the harvesting cost. In the quasi-Newton method, the aim is to determine the harvesting policy which gives maximum profit to the farmers subject to constraints on the maximum amount that can be cut in a 15-day period. The methods are used to determine optimal harvesting policies for the north, central, east, and northeast regions of Thailand for harvesting seasons 2012/13, 2013/14, and 2014/15 based on the data obtained from the Ministry of Industry and the Ministry of Agriculture and Cooperatives of the Royal Thai government.
A laboratory stud:r ,vas made on the relation of wettability and wetting equilibrium to electrical resistivit:r.particularly under dynamic conditions. Teflon cores and sJo'nthetic fluids as well as r4!serYoir cores and fluids were used. Resisth"ities were measured b}" a four-electrode svstem_
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