29 citations · 187 across the 39 of their papers we have counts for
47 papers
On the Laplace equation with non-local dynamical boundary conditions
Raffaela Capitanelli, Mirko D'Ovidio
Aim of the paper is to study non-local dynamic boundary conditions of reactive-diffusive type for the Laplace equation from analytic and probabilistic point of view. In particular,…
On the non-local boundary value problem from the probabilistic viewpoint
Mirko D'Ovidio
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case n…
Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs
Stefano Bonaccorsi, Fausto Colantoni, Mirko D'Ovidio +1
We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random time…
Fractional Boundary Value Problems and elastic sticky Brownian motions, II: Non-local dynamic boundary conditions on smooth domains
Mirko D'Ovidio
We introduce a wide class of sticky Brownian motions (not necessarily Markovian) and study their boundary occupation time through different notions of holding times. This class con…
On the inverse gamma subordinator
Fausto Colantoni, Mirko D'Ovidio
In this paper we deal with some open problems concerned with gamma subordinators. In particular, we provide a representation for the moments of the inverse gamma subordinator. Then…
Elastic drifted Brownian motions and non-local boundary conditions
Mirko D'Ovidio, Francesco Iafrate
We provide a deep connection between elastic drifted Brownian motions and inverses to tempered subordinators. Based on this connection, we establish a link between multiplicative f…
Effects of fractional derivatives in epidemic models
Caterina Balzotti, Mirko D'Ovidio, Anna Chiara Lai +1
We study epidemic Susceptible-Infected-Susceptible models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve acco…
Fractional boundary value problems
Mirko D'Ovidio
We study some functionals associated with a process driven by a fractional boundary value problem (FBVP for short). By FBVP we mean a Cauchy problem with boundary condition written…
Models of space-time random fields on the sphere
Mirko D'Ovidio, Enzo Orsingher, Lyudmyla Sakhno
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymp…
Solutions of Bernoulli equations in the fractional setting
Mirko D'Ovidio, Anna Chiara Lai, Paola Loreti
We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractio…
Non-local logistic equations from the probability viewpoint
Mirko D'Ovidio
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We prov…
On the time fractional heat equation with obstacle
Carlo Alberini, Raffaela Capitanelli, Mirko D'Ovidio +1
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…
Fractional Cauchy problem on random snowflakes
Raffaela Capitanelli, Mirko D'Ovidio
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…
Generalized binomials in fractional calculus
Mirko D'Ovidio, Anna Chiara Lai, Paola Loreti
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 p…
Fractional SIS epidemic models
Caterina Balzotti, Mirko D'Ovidio, Paola Loreti
In this paper we consider the fractional SIS epidemic model (-SIS model) in the case of constant population size. We provide a representation of the explicit solution to the fra…
Age representation of Levy walks: partial density waves, relaxation and first passage time statistics
M. Giona, M. D'Ovidio, D. Cocco +2
Levy walks (LWs) define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks. Alternatively, there i…
Delayed and rushed motions through time change
Raffaela Capitanelli, Mirko D'Ovidio
We introduce a definition of delayed and rushed processes in terms of lifetimes of base processes and time-changed base processes. Then, we consider time changes given by subordina…
Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: a pathway to non-autonomous stochastic differential equations and to fractional diffusion
Mirko D'Ovidio, Silvia Vitali, Vittoria Sposini +4
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the e…
Drifted Brownian motions governed by fractional tempered derivatives
Mirko D'Ovidio, Francesco Iafrate, Enzo Orsingher
Fractional equations governing the distribution of reflecting drifted Brownian motions are presented. The equations are expressed in terms of tempered Riemann--Liouville type deriv…
Modified Fractional Logistic Equation
Mirko D'Ovidio, Paola Loreti, Sima Sarv Ahrabi
In the article [B.J.West, Exact solution to fractional logistic equation, Physica A: Statistical Mechanics and its Applications 429 (2015) 103-108], the author has obtained a funct…
Solutions of fractional logistic equations by Euler's numbers
Mirko D'Ovidio, Paola Loreti
In this paper, we solve in the convergence set, the fractional logistic equation making use of Euler's numbers. To our knowledge, the answer is still an open question. The key poin…
Fractional equations via convergence of forms
Raffaela Capitanelli, Mirko D'Ovidio
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are o…
Determination of order in linear fractional differential equations
Mirko D'Ovidio, Paola Loreti, Alireza Momenzadeh +1
In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The or…
Probabilistic representation formula for the solution of fractional high order heat-type equations
Stefano Bonaccorsi, Mirko D'Ovidio, Sonia Mazzucchi
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random…