Investigating the impact of memory effects on computer virus population dynamics: A fractal–fractional approach with numerical analysis

Avcı, İbrahim; Hussain, Azhar; Kanwal, Tanzeela

doi:10.1016/j.chaos.2023.113845

Cited by 8 publications

(2 citation statements)

References 45 publications

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“…The effectiveness of the model had been illustrated by graphical representation with simulation. Fractional order derivative operators can impact memory effects on population dynamics in computer viruses [30]. The results highlight the memory effect associated with fractional order derivatives, where past states and behaviors continue to influence the system.…”

Section: Fractional Order Calculusmentioning

confidence: 85%

Fractional Order Sequential Minimal Optimization Classification Method

Zhao,

Dai,

Huang

2023

Fractal Fract

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Sequential minimal optimization (SMO) method is an algorithm for solving optimization problems arising from the training process of support vector machines (SVM). The SMO algorithm is mainly used to solve the optimization problem of the objective function of SVM, and it can have high accuracy. However, its optimization accuracy can be improved. Fractional order calculus is an extension of integer order calculus, which can more accurately describe the actual system and get more accurate results. In this paper, the fractional order sequential minimal optimization (FOSMO) method is proposed based on the SMO method and fractional order calculus for classification. Firstly, an objective function is expressed by a fractional order function using the FOSMO method. The representation and meaning of fractional order terms in the objective function are studied. Then the fractional derivative of Lagrange multipliers is obtained according to fractional order calculus. Lastly, the objective function is optimized based on fractional order Lagrange multipliers, and then some experiments are carried out on the linear and nonlinear classification cases. Some experiments are carried out on two-classification and multi-classification situations, and experimental results show that the FOSMO method can obtain better accuracy than the normal SMO method.

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Section: Fractional Order Calculusmentioning

confidence: 85%

Fractional Order Sequential Minimal Optimization Classification Method

Zhao,

Dai,

Huang

2023

Fractal Fract

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“…Classical fractional operators include various forms like Riemann-Liouville, Caputo, Erdelyi-Kober, Hadamard [4][5][6], and so on. These forms were frequently used in the modeling of practical problems of physical and engineering [7][8][9][10][11][12]. Recently, Kilbas et al proposed more general concepts of fractional derivatives called 𝜓-Caputo and 𝜓-Riemann-Liouville fractional derivatives [4], which unified classical definitions into a whole form by drawing into the kernel function.…”

Section: 𝑦(T)mentioning

confidence: 99%

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

Li,

Feng

et al. 2024

Math Methods in App Sciences

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This article examines a new family of (p,q)‐Laplacian type nonlinear fractional impulsive differential coupled equations involving both the ‐Caputo fractional derivative and –Riemann–Liouville fractional integral. With the help of Nehari manifold in critical point theory and fractional calculus properties, we obtain the existence of at least one nontrivial ground state solution for the coupled system with some natural and easily verifiable superlinear conditions on the nonlinearity.

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A Physics informed neural network approach for solving time fractional Black-Scholes partial differential equations

Nuugulu,

Patidar,

Tarla

2024

Optim Eng

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We present a novel approach for solving time fractional Black-Scholes partial differential equations (tfBSPDEs) using Physics Informed Neural Network (PINN) approach. Traditional numerical methods are faced with challenges in solving fractional PDEs due to the non-locality and non-differentiability nature of fractional derivative operators. By leveraging the ideas of Riemann sums and the refinement of tagged partitions of the time domain, we show that fractional derivatives can directly be incorporated into the loss function when applying the PINN approach to solving tfBSPDEs. The approach allows for the simultaneous learning of the underlying process dynamics and the involved fractional derivative operator without a need for the use of numerical discretization of the fractional derivatives. Through some numerical experiments, we demonstrate that, the PINN approach is efficient, accurate and computationally inexpensive particularly when dealing with high frequency and noisy data. This work augments the understanding between advanced mathematical modeling and machine learning techniques, contributing to the body of knowlege on the advancement of accurate derivative pricing models.

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Investigating the impact of memory effects on computer virus population dynamics: A fractal–fractional approach with numerical analysis

Cited by 8 publications

References 45 publications

Fractional Order Sequential Minimal Optimization Classification Method

Fractional Order Sequential Minimal Optimization Classification Method

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

A Physics informed neural network approach for solving time fractional Black-Scholes partial differential equations

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