Tychonoff Solutions of the Time-Fractional Heat Equation

Ascione, Giacomo

doi:10.3390/fractalfract6060292

Cited by 4 publications

(5 citation statements)

References 48 publications

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“…(2) it has independent increments with respect to the partial ordering on R N + , i.e. for any choice of 0 = t (0) t (1) t (2) • • • t (k) , the random variables X t (j) − X t (j−1) , j = 1, . .…”

Section: 1mentioning

confidence: 99%

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Some families of random fields related to multiparameter Lévy processes

Iafrate¹,

Ricciuti²

2022

Preprint

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N . We here consider a class of random fields (Xt) t∈R N + which are known as Multiparameter Lévy processes. Related multiparameter semigroups of operators and their generators are represented as pseudo-differential operators. We also consider the composition of (Xt) t∈R N + by means of the so-called subordinator fields and we provide a Phillips formula. We finally study the composition of (Xt) t∈R N + by means of the so-called inverse random fields, which gives rise to interesting long range dependence properties. As a byproduct of our analysis, we study a model of anomalous diffusion in an anisotropic medium which extends the one treated in [8].

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Section: 1mentioning

confidence: 99%

“…The reason they are called in this way is that they enjoy, in some sense, independence and stationarity of increments. Independence of increments is meant in the following way: once established a partial ordering on R N + , for any choice of ordered points t (1) , t (2) , . .…”

Section: Introductionmentioning

confidence: 99%

Some families of random fields related to multiparameter Lévy processes

Iafrate¹,

Ricciuti²

2022

Preprint

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“…Currently, fractional differential equations are also used, which allow considering the memory effect in the dynamics of the model since the fractional operators are non-local. As the memory effect is present in epidemic situations, mainly with the aim of taking advantage of previous experiences to contain the spread of the disease, it is important to consider this effect in the dynamics of the model [1,2,5,13,19].…”

Section: Introductionmentioning

confidence: 99%

“…In addition to epidemiological and applied mathematics in general, fractional calculus has been highlighted in several applications of physics, chemistry, biology, engineering and other areas. Moreover, an attractive feature of fractional models is the better ability to fit data than classical models [1,2,5].…”

Section: Introductionmentioning

confidence: 99%

A Logistic Fractional Model with Control Measures for Cumulative Cases of COVID-19

Lopes

Pedro

Sánchez

et al. 2023

TCAM

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The curve of cumulative cases of individuals infected by COVID-19 shows similar growth to the logistic curve in the period referring to each epidemic "wave'', as each peak of active cases is called. Considering that in pandemic scenarios it is common to seek control measures based on previous experiences. In this paper, we model the curve of cumulative cases through a logistic model with infected removal to include the control measures in the dynamics. This model is based on fractional differential equations to also include the memory effect. We study the scenario of the first two "waves'' in the analyzed countries: Brazil, China, Italy, and Switzerland. Scenarios with and without control measures are compared, proving the importance of control measures such as isolation. Moreover, this model makes it possible to determine the portion of the population that did not participate in the dynamics of the spread of the disease, as well as to analyze how the number of infected people reduced in each country.

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“…X 0 = 0 a.s. 2. It has independent increments with respect to the partial ordering on R N + , i.e., for any choice of 0 = t (0) t (1) t (2) • • • t (k) , the random variables X t ( j) − X t ( j−1) , j = 1, . .…”

mentioning

confidence: 99%

Some Families of Random Fields Related to Multiparameter Lévy Processes

Iafrate,

Ricciuti

2024

J Theor Probab

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Let $${\mathbb {R}}^N_+= [0,\infty )^N$$ R + N = [ 0 , ∞ ) N . We here make new contributions concerning a class of random fields $$(X_t)_{t\in {\mathbb {R}}^N_+}$$ ( X t ) t ∈ R + N which are known as multiparameter Lévy processes. Related multiparameter semigroups of operators and their generators are represented as pseudo-differential operators. We also provide a Phillips formula concerning the composition of $$(X_t)_{t\in {\mathbb {R}}^N_+}$$ ( X t ) t ∈ R + N by means of subordinator fields. We finally define the composition of $$(X_t)_{t\in {\mathbb {R}}^N_+}$$ ( X t ) t ∈ R + N by means of the so-called inverse random fields, which gives rise to interesting long-range dependence properties. As a byproduct of our analysis, we present a model of anomalous diffusion in an anisotropic medium which extends the one treated in Beghin et al. (Stoch Proc Appl 130:6364–6387, 2020), by improving some of its shortcomings.

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Tychonoff Solutions of the Time-Fractional Heat Equation

Cited by 4 publications

References 48 publications

Some families of random fields related to multiparameter Lévy processes

Some families of random fields related to multiparameter Lévy processes

A Logistic Fractional Model with Control Measures for Cumulative Cases of COVID-19

Some Families of Random Fields Related to Multiparameter Lévy Processes

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