Multi-fractional generalized Cauchy process and its application to teletraffic

Li, Ming

doi:10.1016/j.physa.2019.123982

Cited by 49 publications

(39 citation statements)

References 86 publications

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“…It is worth noting that the Mittag-Leffler functions in Definition 2.1 may be represented by the elementary functions expressed in [37] as well. Meanwhile, the proposed method may be a substantial help in many other researches such as computing the multifractal dimension of network traffic investigated in [38].…”

Section: Discussionmentioning

confidence: 99%

Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system

Heydari

Avazzadeh

2020

Engineering with Computers

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In this paper, the Chebyshev-Gauss-Lobatto collocation method is developed for studying the variable-order (VO) time fractional model of the generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves. To define this new system, the Atangana-Baleanu fractional operator is implemented. The operational matrix of VO fractional differentiation for the shifted Chebyshev polynomials is extracted and then, a collocation scheme is established to reduce the original VO fractional problem to a system of nonlinear algebraic equations. The validity of the presented method is investigated on two numerical examples.

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Section: Discussionmentioning

confidence: 99%

Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system

Heydari

Avazzadeh

2020

Engineering with Computers

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“…Note that h(t) is a solution to a fractional-order system (Li et al [51,53]). We see that a system that produces phytoplankton movement patterns in marine biology is of fractional-order.…”

Section: Appendix a Fractal Analysis Of Time Series Of Phytoplankton Movement Patternsmentioning

confidence: 99%

Fat Tail in the Phytoplankton Movement Patterns and Swimming Behavior: New Insights into the Prey-Predator Interactions

Xiao

et al. 2021

Fractal Fract

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Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in diverse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimming behavior of phytoplankton in response to the food supply were studied. The log-normal distribution was used for fitting the probability density values of the movement data of Oxyrrhis marina. Results showed that obvious fat tails exist in the movement patterns of O. marina without and with positive stimulations of food supply. The algal cells tended to show a more chaotic and disorderly movement, with shorter and neat steps after adding the food source. At the same time, the randomness of turning rate, path curvature and swimming speed increased in O. marina cells with food supply. Generally, the responses of phytoplankton movement were stronger when supplied with direct prey cells rather than the cell-free filtrate. The scale-free random movements are considered to benefit the adaption of the entire phytoplankton population to varied environmental conditions. Inferentially, the movement pattern of O. marina should also have the characteristics of long-range dependence, local self-similarity and a system of fractional order.

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“…In fact, fractional derivative and integral operators, due to higher degree of freedom in comparison to the classical operators as well as their memory and nonlocal properties, have received many applications in various problems [4]. For instance, some important works related to recent developments in fractional calculus and its applications can be found in [5][6][7][8][9][10]. The reader should note that the most important issue about problems involving such operators is finding their exact solutions, which is often very difficult and may even be impossible.…”

Section: Introductionmentioning

confidence: 99%

An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

Heydari

Atangana

2021

Adv Differ Equ

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This paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order fractional version of the Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family of basis functions, are employed to generate an operational matrix method for this equation. A new fractional operational matrix related to these polynomials is extracted and employed to construct the presented method. Using this approach, an algebraic system of equations is obtained instead of the original variable-order equation. The numerical solution of this system can be found easily. Some numerical examples are provided for verifying the accuracy of the generated approach.

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Multi-fractional generalized Cauchy process and its application to teletraffic

Cited by 49 publications

References 86 publications

Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system

Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system

Fat Tail in the Phytoplankton Movement Patterns and Swimming Behavior: New Insights into the Prey-Predator Interactions

An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

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