Fractional derivative truncation approximation for real-time applications

Duhé, Jean-François; Victor, Stéphane; Melchior, Pierre; Abdelmounen, Youssef; Roubertie, François

doi:10.1016/j.cnsns.2023.107096

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…Infectious disease research utilizes classical mathematical models with integer-order derivatives, see [31][32][33][34]. Fractional derivatives, however, are advantageous in mathematical models due to their non-locality or long-memory properties [35,36]. COVID-19 dynamics in Lagos, Nigeria, for instance, are described in [37].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

et al. 2023

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In this study, we provide a fractional-order mathematical model that considers the effect of vaccination on COVID-19 spread dynamics. The model accounts for the latent period of intervention strategies by incorporating a time delay τ. A basic reproduction number, R0, is determined for the model, and prerequisites for endemic equilibrium are discussed. The model’s endemic equilibrium point also exhibits local asymptotic stability (under certain conditions), and a Hopf bifurcation condition is established. Different scenarios of vaccination efficacy are simulated. As a result of the vaccination efforts, the number of deaths and those affected have decreased. COVID-19 may not be effectively controlled by vaccination alone. To control infections, several non-pharmacological interventions are necessary. Based on numerical simulations and fitting to real observations, the theoretical results are proven to be effective.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

et al. 2023

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“…Fractional calculus has received increasing attention in recent decades due to its ability to capture the memory effect of various phenomena (Duhé et al ., 2023; Beigmohamadi et al ., 2022). In traditional grey models, the ordinary derivative du ( t )/ dt captures only the instantaneous change in a dynamic system, disregarding its memory effect (Kang et al ., 2022).…”

Section: Introductionmentioning

confidence: 99%

Memory-dependent derivative grey Bernoulli model and its application in electricity generation forecast

Zhang,

Li,

et al. 2023

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PurposeThis paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.Design/methodology/approachThis paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.FindingsThe selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.Research limitations/implicationsThe model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.Practical implicationsIn practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.Originality/valueBased on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

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“…Fractional calculus is the mathematical study of the characteristics of integral and differential operators with real or complex orders [1]. When modeling processes or systems that have memory or are nonlocal, the techniques of fractional calculus may be quite helpful [2]. Different forms of fractional integrals and differential operators have been suggested by mathematicians such as Riemann, Liouville, Grunwald, Letnikov, Sonine, Marchaud, Weyl, Riesz, Hadamard, Kober, Erdelyi, Caputo, and many more.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2023

Progr. Fract. Differ. Appl.

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The authors of this paper take a fractional calculus approach to the Casagrandi and Rinaldi mathematical model of tourists in an area or country. The tourism model uses an ordinary differential equation to investigate the number of tourists in the area, the quality of natural resources, and the amounts invested in tourist infrastructure. For each scenario in the model, the ordinary differential equations are fractionalized using the Caputo derivative of a function with respect to a specific exponential function. In each example, we incorporate the concept of fractionalization in conjunction with a specific exponential function in order to change the model. As a result, various hypotheses are elicited by allowing some adjustments to the initial parameters. The results are further displayed by plotting Mittag-Leffler function graphs for various parameters and comparing them to the original solutions. The graphs' analysis investigates the behaviour of the modified model's solution; in this study, all modified model solutions are of the Mittag -Leffler form, whereas all original models solve using an exponential function. The assumptions and changes in parameters cause minor changes in the behaviour of the solutions.

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Fractional derivative truncation approximation for real-time applications

Cited by 8 publications

References 22 publications

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

Memory-dependent derivative grey Bernoulli model and its application in electricity generation forecast

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