Related papers: A subordination principle on Wright functions and …
In this paper we study pseudo-processes related to odd-order heat-type equations composed with L\'evy stable subordinators. The aim of the article is twofold. We first show that the pseudo-density of the subordinated pseudo-process can be…
We analyze the $\beta$-functions of Yukawa and electromagnetic theories with Lorentz violation (LV) and propose an alternative method to find the scale dependence of the different fields that parametrize such violations. The method of…
We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to…
In this note we show how a initial value problem for a relaxation process governed by a differential equation of non-integer order with a constant coefficient may be equivalent to that of a differential equation of the first order with a…
We collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case. We focus here on some issues…
Variational convexity, together with ist strong counterpart, of extended-real-valued functions has been recently introduced by Rockafellar. In this paper we present second-order characterizations of these properties, i.e., conditions using…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem…
We consider a new family of $\R^d$-valued L\'{e}vy processes that we call Lamperti stable. One of the advantages of this class is that the law of many related functionals can be computed explicitely (see for instance \cite{cc}, \cite{ckp},…
In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also…
In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its…
In this review paper we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics.We first start with the analytical properties of the classical Wright functions of which…
We use sequences which depend on two parameters to define families of ultradifferentiable functions which contain Gevrey classes. It is shown that such families are closed under superposition, and therefore inverse closed as well.…
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional…
The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives…
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the…