A NEW FRACTAL FRACTIONAL MODELING OF THE COMPUTER VIRUSES SYSTEM

Mohammad Partohaghighi, Abdullahi Yusuf, Yeliz Karaca, Yong-Min Li, Tarek F. Ibrahim, B. A. Younis, Bahaa Saleh and Ayman A. Aly
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Mohammad Partohaghighi: Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA
Abdullahi Yusuf: ��Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey‡Department of Mathematics, Near East University TRNC, Mersin 10, 99138, Nicosia, Turkey
Yeliz Karaca: �University of Massachusetts Medical School, Worcester, MA 01655, USA
Yong-Min Li: �Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China∥Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China
Tarek F. Ibrahim: *Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha, Saudi Arabia††Department of Mathematics, Faculty of Science, Mansoura University, Egypt
B. A. Younis: ��‡Department of Mathematics, Faculty of Sciences and Arts in Zahran Alganoob, King Khalid University, Abha, Saudi Arabia
Bahaa Saleh: �§Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia
Ayman A. Aly: �§Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-19

Abstract: In this study, we model the fractal-fractional system of the Computer virus problem using the Atangana–Baleanu operator. Moreover, we have presented the existence and the uniqueness of the results under applying the Schauder fixed point and Banach fixed theorems. We have used the Atangana–Toufik technique to obtain the approximate solutions by choosing various values of orders. Different values of fractal-fractional orders along with different amounts of initial conditions are selected to examine the performance of the suggested numerical method on the new fractal-fractional system. Also, graphs in different dimensions are presented to exhibit the solutions, clearly.

Keywords: Mittag-Leffler Kernel; Numerical Method; Fractional Computer Virus Model (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401843

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DOI: 10.1142/S0218348X22401843

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