Asumu Fractional Derivative Applied to Edge Detection on SARS-COV2 Images

Edge detection consists of a set of mathematical methods which identifies the points in a digital image where image brightness changes sharply. In the traditional edge detection methods such as the first-order derivative filters, it is easy to lose image information details and the second-order derivative filters are more sensitive to noise. To overcome these problems, the methods based on the fractional differential-order filters have been proposed in the literature. This paper presents the construction and implementation of the Prewitt fractional differential filter in the Asumu definition sense for SARS-COV2 image edge detection. The experiments show that these filters can avoid noise and detect rich edge details. The experimental comparison show that the proposed method outperforms some edge detection methods. In the next paper, we are planning to improve and combine the proposed filters with artificial intelligence algorithm in order to program a training system for SARS-COV2 image classification with the aim of having a supplemental medical diagnostic.

Asymptotics solutions of a singularly perturbed integro-differential fractional order derivative equation with rapidly oscillating coefficients

In this paper, the regularization method of S.A.Lomov is generalized to the singularly perturbed integrodifferential fractional-order derivative equation with rapidly oscillating coefficients. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution to this problem. The case of the absence of resonance is considered, i.e. the case when an integer linear combination of a rapidly oscillating inhomogeneity does not coincide with a point in the spectrum of the limiting operator at all points of the considered time interval. The case of coincidence of the frequency of a rapidly oscillating inhomogeneity with a point in the spectrum of the limiting operator is called the resonance case. This case is supposed to be studied in our subsequent works. More complex cases of resonance (for example, point resonance) require more careful analysis and are not considered in this work.

Solutions and memory effect of fractional-order chaotic system: A review (Interdisciplinary Physics)

Fractional calculus is a 300 years topic, which has been introduced to real physics systems modeling and engineering applications. In the last few decades, fractional-order nonlinear chaotic systems have been widely investigated. Firstly, the most used methods to solve fractional-order chaotic systems are reviewed. Characteristics and memory effect in those method are summarized. Then we discussed the memory effect in the fractional-order chaotic systems through the fractional-order calculus and numerical solution algorithms. It shows that the integer-order derivative has full memory effect, while the fractional-order derivative has nonideal memory effect due to the kernel function. Memory lose and short memory are discussed. Finally, applications of the fractional-order chaotic systems regarding the memory effects are investigated. The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.