Showing papers by "Mirko D'Ovidio published in 2020"
TL;DR: In this article, the authors consider time changes given by subordinators and their inverse processes and show that inverse processes are not necessarily leading to delayed processes, quite surprisingly, they are not always leading to faster processes.
Abstract: We consider time changes given by subordinators and their inverse processes. Our analysis shows that, quite surprisingly, inverse processes are not necessarily leading to delayed processes.
20 citations
31 Aug 2020
TL;DR: In this article, the authors considered the fractional SIS epidemic model (α-SIS model) in the case of constant population size and provided a representation of the explicit solution to the fraction fractional model and illustrate the results by numerical schemes.
Abstract: In this paper, we consider the fractional SIS (susceptible-infectious-susceptible) epidemic model (α-SIS model) in the case of constant population size. We provide a representation of the explicit solution to the fractional model and we illustrate the results by numerical schemes. A comparison with the limit case when the fractional order α converges to 1 (the SIS model) is also given. We analyze the effects of the fractional derivatives by comparing the SIS and the α-SIS models.
16 citations
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TL;DR: In this article, the authors considered the fractional SIS epidemic model in the case of constant population size and analyzed the effects of fractional derivatives by comparing the SIS and the $\alpha$-SIS models.
Abstract: In this paper we consider the fractional SIS epidemic model ($\alpha$-SIS model) in the case of constant population size. We provide a representation of the explicit solution to the fractional model and we illustrate the results by numerical schemes. A comparison with the limit case when the fractional order $\alpha \uparrow 1$ (the SIS model) is also given. We analyse the effects of the fractional derivatives by comparing the SIS and the $\alpha$-SIS models.
4 citations
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TL;DR: In this article, a Caputo time fractional degenerate diffusion equation was shown to be equivalent to the fractional parabolic obstacle problem, and its solution evolves for any α = 0, 1 to the same stationary state, the solution of the classic elliptic obstacle problem.
Abstract: We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for any $\alpha\in(0,1)$ to the same stationary state, the solution of the classic elliptic obstacle problem. The only thing which changes with $\alpha$ is the convergence speed. We also study the problem from the numerical point of view, comparing some finite different approaches, and showing the results of some tests. These results extend what recently proved in [1] for the case $\alpha=1$.
2 citations
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TL;DR: In this article, a class of generalized binomials emerging in fractional calculus is considered, for which several ready-for-use combinatorial identities, including an adapted version of the Pascal's rule, are provided.
Abstract: We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities, including an adapted version of the Pascal's rule. We then investigate the associated generating functions, for which we establish a recursive, combinatorial and integral formulation. From this, we derive an asymptotic version of the Binomial Theorem. A combinatorial and asymptotic analysis of some finite sums completes the paper.
2 citations
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TL;DR: The explicit representation and the numerical schemes for the limit case of the fractional order $\alpha\uparrow1$, corresponding to the well-known ordinary SIS model, are examined.
Abstract: This work deals with the fractional SIS epidemic model in the case of constant population size. We provide a representation of the explicit solution to the fractional model under suitable assumptions and we validate the results by considering two numerical schemes. We examine the explicit representation and the numerical schemes for the limit case of the fractional order $\alpha\uparrow1$, corresponding to the well-known ordinary SIS model, and we analyse the effects of the fractional derivatives by comparing the two models.
1 citations
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TL;DR: In this paper, the fractional Cauchy problem with Robin condition on the pre-fractal boundary was studied and asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain were obtained.
Abstract: We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the pre-fractal boundary obtaining asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain.