• We propose a discrete fractional order model to analyze the behaviour of an epidemic process with indirect transmission. Our main contribution is study influence and memory steps on solution. The stability around equilibrium points our analyzed. obtain some bounds tan introduction derivhe population size assure nonnegativity solution model. A proposed This based version Grunwald-Letnikov deri...

Underwater images usually suffer from degraded visibility. Light attenuates and scatters in water resulting in low contrast and haziness in the scenes. Therefore, the main problems to be dealt with in underwater environment are poor contrast, non-uniform lighting, haziness and blurring. Hence, in order to study underwater images, it becomes utmost important to extract the invisible or unclear e...

This paper presents a novel adaptive fuzzy logic controller (FLC) equipped with an adaptive algorithm to achieve synchronization performance for fractional chaotic systems. By introducing the fuzzy control design and robustness tracking approach, a desired synchronization error can be attenuated to a prescribed level, even in the presence of the high level of uncertainties and noisy training da...

System identification is important in science and engineering. This contribution proposes a simple yet elegant scheme for identifying a fractional order dynamic system based on its observed response to a standard excitation. Our approach consists in obtaining and solving a set of simultaneous linear equations connecting the parameters to yield the desired estimates. To minimise the effect of no...

This paper introduces a numerical technique for the estimation of stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise excitation. The Wiener-Hermite expansion is integrated with the Grunwald-Letnikov approximation in case of fractional order damping and with Coimbra approximation in case of variableorder damping. The numerical solver...

In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grünwald–Letnikov derivative, the Riemann–Liouville derivative and the Caputo derivative. Especially, we compare the Riemann–Liouville derivative with the Caputo derivative. And sequential property of the Caputo derivative is also derived, which is helpful in translating the higher fractional-order di...

and Applied Analysis 3 Definition 2. The Grünwald-Letnikov fractional derivative with order α of function x(t) is defined below:

The formulations of Riemann-Liouville and Caputo derivatives in the complex plane are presented. Two versions corresponding to the whole or half plane. It is shown that they can be obtained from the Grünwald-Letnikov derivative.

Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most papers been related to simulated results on system dynamics rather than their hardware implementations. This work reports implementation a new memristor map with “hidden attractors”. The is developed based memristive by using Grunwald–Letnikov difference operator. has flexible fixed point...