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Fractal Fract
Volume 9
Issue 2
10.3390/fractalfract9020090
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Probing Malware Propagation Model with Variable Infection Rates Under Integer, Fractional, and Fractal–Fractional Orders

by
Nausheen Razi
1,
Ambreen Bano
2,
Umar Ishtiaq
3,*,
Tayyab Kamran
1,
Mubariz Garayev
4 and
Ioan-Lucian Popa
5,6,*
1
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2
Department of Mathematics and Statistics, Ripha International University, Haj Complex I-14, Islamabad 44000, Pakistan
3
Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan
4
Department of Mathematics, College of Science, King Saud University, Riyadh P.O. Box 2455, Saudi Arabia
5
Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
6
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2025, 9(2), 90; https://doi.org/10.3390/fractalfract9020090 (registering DOI)
Submission received: 12 December 2024 / Revised: 21 January 2025 / Accepted: 22 January 2025 / Published: 1 February 2025
(This article belongs to the Special Issue Advances in Fractional Order Derivatives and Their Applications, 3rd Edition)
Versions Notes

Abstract

Malware software has become a pervasive threat in computer and mobile technology attacks. Attackers use this software to obtain information about users of the digital world to obtain benefits by hijacking their data. Antivirus software has been developed to prevent the propagation of malware, but this problem is not yet under control. To develop this software, we have to check the propagation of malware. In this paper, we explore an advanced malware propagation model with a time-delay factor and a variable infection rate. To better understand this model, we use fractal–fractional theory. We use an exponential decay kernel for this. For theoretical purposes (existence, uniqueness, and stability), we use the results from fixed-point theory, and, for numerical purposes, a Lagrange two-point interpolation polynomial is used to develop an algorithm. Matlab R2016a is used for simulation, and the physical significance is assessed. We examine the impact of different fractal and fractional orders for various parameters. Moreover, we compare four different mathematical models (classical, fractional, fractal, and fractal–fractional). Also, constant and variable fractional and fractal orders are compared using graphs. We investigate the idea that significant perturbation in infected nodes might be due to minor changes. This work may help with developing antivirus strategies in real life.
Keywords: malware propagation; exponential decay kernel; fractal–fractional orders; variable infection rate; numerical simulation; constant and variable fractional order; constant and variable fractal order malware propagation; exponential decay kernel; fractal–fractional orders; variable infection rate; numerical simulation; constant and variable fractional order; constant and variable fractal order

Share and Cite

MDPI and ACS Style

Razi, N.; Bano, A.; Ishtiaq, U.; Kamran, T.; Garayev, M.; Popa, I.-L. Probing Malware Propagation Model with Variable Infection Rates Under Integer, Fractional, and Fractal–Fractional Orders. Fractal Fract. 2025, 9, 90. https://doi.org/10.3390/fractalfract9020090

AMA Style

Razi N, Bano A, Ishtiaq U, Kamran T, Garayev M, Popa I-L. Probing Malware Propagation Model with Variable Infection Rates Under Integer, Fractional, and Fractal–Fractional Orders. Fractal and Fractional. 2025; 9(2):90. https://doi.org/10.3390/fractalfract9020090

Chicago/Turabian Style

Razi, Nausheen, Ambreen Bano, Umar Ishtiaq, Tayyab Kamran, Mubariz Garayev, and Ioan-Lucian Popa. 2025. "Probing Malware Propagation Model with Variable Infection Rates Under Integer, Fractional, and Fractal–Fractional Orders" Fractal and Fractional 9, no. 2: 90. https://doi.org/10.3390/fractalfract9020090

APA Style

Razi, N., Bano, A., Ishtiaq, U., Kamran, T., Garayev, M., & Popa, I.-L. (2025). Probing Malware Propagation Model with Variable Infection Rates Under Integer, Fractional, and Fractal–Fractional Orders. Fractal and Fractional, 9(2), 90. https://doi.org/10.3390/fractalfract9020090

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