Generalised Fractional Evolution Equations of Caputo Type

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. \\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.Comment: To be published in 'Chaos, Solitons & Fractals

A 3-3-1 model with right-handed neutrinos based on the Δ(27)\Delta\left(27\right) family symmetry

We present the first multiscalar singlet extension of the 3-3-1 model with right-handed neutrinos, based on the $\Delta \left( 27\right)$ family symmetry, supplemented by the $Z_{4}\otimes Z_{8}\otimes Z_{14}$ flavor group, consistent with current low energy fermion flavor data. In the model under consideration, the light active neutrino masses are generated from a double seesaw mechanism and the observed pattern of charged fermion masses and quark mixing angles is caused by the breaking of the $\Delta \left( 27\right) \otimes Z_{4}\otimes Z_{8}\otimes Z_{14}$ discrete group at very high energy. Our model has only 14 effective free parameters, which are fitted to reproduce the experimental values of the 18 physical observables in the quark and lepton sectors. The obtained physical observables for the quark sector agree with their experimental values, whereas those ones for the lepton sector also do, only for the inverted neutrino mass hierarchy. The normal neutrino mass hierarchy scenario of the model is disfavored by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of $m_{\beta \beta }=$ 22 meV, a leptonic Dirac CP violating phase of $34^{\circ }$ and a Jarlskog invariant of about $10^{-2}$ for the inverted neutrino mass spectrum.Comment: 22 pages. Final version published in European Physical Journal C. arXiv admin note: text overlap with arXiv:1601.03300, arXiv:1309.656

Interpolation sets in spaces of continuous metric-valued functions

Let $X$ and $M$ be a topological space and metric space, respectively. If $C(X,M)$ denotes the set of all continuous functions from X to M, we say that a subset $Y$ of $X$ is an \emph{$M$-interpolation set} if given any function $g\in M^Y$ with relatively compact range in $M$, there exists a map $f\in C(X,M)$ such that $f_{|Y}=g$. In this paper, motivated by a result of Bourgain in \cite{Bourgain1977}, we introduce a property, stronger than the mere \emph{non equicontinuity} of a family of continuous functions, that isolates a crucial fact for the existence of interpolation sets in fairly general settings. As a consequence, we establish the existence of $I_0$ sets in every nonprecompact subset of a abelian locally $k_{\omega}$-groups. This implies that abelian locally $k_{\omega}$-groups strongly respects compactness

Topological gravitation on graph manifolds

A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the topological structure of our universe.Comment: 3 pages, a talk delivered at the 11th Marcel Grossmann Meeting (2006