in this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. we analyze the existence and stability of all possibleequilibria. numerical simulations reveal that anti-predator behaviour notonly makes the coexistence of the prey and predator po...

Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach b...

Obesity and insulin resistance are highly prevalent in subjects diagnosed with sleep apnea. One factor common to obesity, sleep and insulin resistance is autonomic nervous system dysfunction, in particular, sympathetic overactivity. Although the causal links among these factors are not well understood, it is likely that the vicious cycle of interplay among these factors predisposes to the emerg...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

1. J. Burbea, Sharp inequalities for holomorphic functions, Illinois J. Math. 31 (1987) 248–264. 2. T. Carleman, Zur Theorie der Minimalflächen, Math. Z. 9 (1921) 154–160. 3. P. L. Duren, Theory of H p Spaces, Academic Press, New York, 1970; reprinted by Dover, Mineola, NY, 2000. 4. T. W. Gamelin and D. Khavinson, The isoperimetric inequality and rational approximation, this MONTHLY 96 (1989) 1...

This article presents a robust control design method on frequency domain using Mathematica for regularization of glucose level in Type I diabetes persons under intensive care. The method originally proposed under Mathematica by Helton and Merino (1998) is now improved with a disturbance rejection constraint inequality, and is tested on the three-state minimal model. Nonlinear closed loop simula...

In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...