A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Mohammad, Mutaz

doi:10.3390/sym11070854

Cited by 23 publications

(17 citation statements)

References 31 publications

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“…For analysis, Wepawet was employed to identify CVE-IDs in the web pages, and the National Vulnerability Database (NVD) provided information concerning the CVEs. To improve detection rates they are reduced unnecessary information by a grouping algorithm [26]. Features were then extracted and the prediction model computed malwaredownloading probabilities.…”

Section: 7mentioning

confidence: 99%

Detection and Analysis of Drive-by Downloads and Malicious Websites

Ibrahim

Herami

Naqbi

et al. 2020

Communications in Computer and Information Science

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A drive-by download is a download that occurs without users action or knowledge. It usually triggers an exploit of vulnerability in a browser to downloads an unknown file. The malicious program in the downloaded file installs itself on the victims machine. Moreover, the downloaded file can be camouflaged as an installer that would further install malicious software. Drive-by downloads is a very good example of the exponential increase in malicious activity over the Internet and how it affects the daily use of the web. In this paper, we try to address the problem caused by drive-by downloads from different standpoints. We provide in-depth understanding of the difficulties in dealing with drive-by downloads and suggest appropriate solutions. We propose machine learning and feature selection solutions to remedy the drive-by download problem. Experimental results reported 98.2% precision, 98.2% F-Measure and 97.2% ROC area.

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Section: 7mentioning

confidence: 99%

Detection and Analysis of Drive-by Downloads and Malicious Websites

Ibrahim

Herami

Naqbi

et al. 2020

Communications in Computer and Information Science

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“…This provides us with simple and better reconstruction of the coefficients to obtain the corresponding unknown elements of the space L 2 (R) and also gives us better accuracy order and relatively small errors. In practice, framelet-based methods have been applied to provide accurate and efficient numerical schemes for solving several types of integral and differential equations; see, for example, [49][50][51][52][53][54][55][56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Fractional nonlinear Volterra–Fredholm integral equations involving Atangana–Baleanu fractional derivative: framelet applications

Mohammad

Trounev

2020

Adv Differ Equ

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In this work, we propose a framelet method based on B-spline functions for solving nonlinear Volterra–Fredholm integro-differential equations and by involving Atangana–Baleanu fractional derivative, which can provide a reliable numerical approximation. The framelet systems are generated using the set of B-splines with high vanishing moments. We provide some numerical and graphical evidences to show the efficiency of the proposed method. The obtained numerical results of the proposed method compared with those obtained from CAS wavelets show a great agreement with the exact solution. We confirm that the method achieves accurate, efficient, and robust measurement.

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“…This is largely due to the fact that wavelets have the right structure to capture the sparsity in 'physical' images, perfect mathematical properties such as its multi-scale structure, sparsity, smoothness, compactly supported, and high vanish moments. It has many applications in fractional integral and differential equations (see for example [11][12][13][14][15][16][17][18][19][20][21]. Riesz wavelets in L 2 (R) have been used extensively in the context of both pure and numerical analysis in many applications, due to their well prevailing and recognized theory and its natural properties such as sparsity and stability which lead to a well-conditioned scheme.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation

Mohammad

Trounev

Cattani

2020

Preprint

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The well-known novel virus (COVID-19) is a new strain of coronavirus which considered by the World Health Organization (WHO) as a dangerous epidemic. More than 3.5 million positive cases and 250 thousand deaths (up to May 5, 2020) caused by COVID-19 and has affected more than 280 countries over the world. Therefore, studying the prediction of this virus spreading in further attracts a major public attention. In the United Arab Emirates (UAE), up to same date, there are 14730 positive cases and 137 deaths according to national authorities. In this work, we study a dynamical model based on fractional derivative of nonlinear equations that describe the outbreak of COVID-19 according to the available infection data announced and approved by the national committee in the press. We simulate the available total cases reported based on Riesz wavelets generated by some refinable functions, namely the smoothed pseudo-splines of type I and II with high vanishing moments. Based on these data, we also consider the formulation of the pandemic model using Caputo fractional derivative definition. We then solve numerically the nonlinear system that describe the dynamics of COVID-19 with the given resources based on the collocation Riesz wavelet system constructed. We present graphical illustrations of the numerical solutions of all parameter of the model being handled under different situations. It is anticipated that these results will contribute to the ongoing research to reduce the spreading of the virus and infection cases.

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A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Cited by 23 publications

References 31 publications

Detection and Analysis of Drive-by Downloads and Malicious Websites

Detection and Analysis of Drive-by Downloads and Malicious Websites

Fractional nonlinear Volterra–Fredholm integral equations involving Atangana–Baleanu fractional derivative: framelet applications

The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation

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