The fractional-order derivative and integral of Grünwald Letnikov's definition are implemented based on FPGA for different fractional orders. A new algorithm is proposed to implement the GL integral based on linear approximation approach, where the memory dependency of the fractional order systems is eliminated. Moreover, the linear approximation design shows an improvement of 91% and 92% in the

A new approximation method of the fractional-order Laplacian operator sα is introduced. The approximation is based on a weighted sum of first-order filter sections and its analytical proof is given. The optimal high-pass filter section parameters that cover six frequency decades are obtained using the flower pollination algorithm while the effect of the number of filter sections on the accuracy of

Recently, the triple-lobe behavior is found in the I-V characteristics of some memristive devices generating another non-zero pinchoff point. In this paper, a flux-controlled memristive model is developed to generate the triple-lobe behavior (double pinchoff points) based on a fractional second-order model. The conditions for observing triple lobes are derived besides the coordinates of the

This work presents a novel fractional H8 robust indirect adaptive fuzzy logic control strategy based on the variable structure control theory design (FRAFC-VSC) to synchronize two fractional-order chaotic systems. The contribution of this work is the use of an adaptive fractional order PI-regulator and a saturation function to eliminate the chattering phenomena in the control and surface signals

In this paper, we propose a new hyperchaotic temperature fluctuations model and describe its modelling in detail. We study the characteristics of the new hyperchaotic temperature fluctuations model such as its phase portraits, rest points, symmetry, invariance, Lyapunov characteristic exponents, bifurcation analysis, etc. In fact, it is shown that the new temperature fluctuations model has a self

This paper introduces a Fractional-Order Model (FOM) of Up-flow Anaerobic Sludge Blanket (UASB) reactor for wastewater treatment regarding high-strength substrate biodegradation. The model can investigate the biogas production rate as well as the specific growth rate of bacteria with extra degree of freedom. Also, the hereditary effect of resident biomass on substrate degradation is studied on

Background: Photodynamic therapy (PDT) has been determined to be a promising treatment modality in the most resistant tumors such as malignant melanoma. However, the key cytotoxic agent of PDT, -singlet oxygen (1O2) - represents a high risk of photodynamic-associated side effects e.g. skin photosensitization. Recently, controllable photosensitization, where 1O2 is produced on demand, has received

Recently, numerous research works in retinal-structure analysis have been performed to analyze retinal images for diagnosing and preventing ocular diseases such as diabetic retinopathy, which is the first most common causes of vision loss in the world. In this paper, an algorithm for vessel detection in fundus images is employed. First, a denoising process using the noise-estimation-based

Controlling a nonlinear, time-varying, uncertain, coupled multiinput-multioutput (MIMO) complex system is always a challenging task for control engineers. A linear PID controller is not able to control effectively these complex systems and a robust adaptive controller is needed for perfect control. In this chapter, a fractional order fuzzy sliding mode proportional derivative (FOFSMCPD) controller

During the last 10 years, fractional calculus has find its application in almost every field of science and engineering. One of the well-studied application area is control engineering. Fractional calculus gives a more realistic modeling of linear and nonlinear systems which are called as fractional order systems. Fractional order control is another area of study under this field. Fractional order