Related papers: Towards multifractional calculus
The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.
We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1-forms and associated semigroups are considered. Their probabilistic interpretation…
In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…
In this paper we connect classical differential geometry with the concepts from geometric calculus. Moreover, we introduce and analyze a more general Laplacian for multivector-valued functions on manifolds. This allows us to formulate a…
We investigate the fractional magnetic $p$-Laplacian operator in the physical dimension case $N=3$, with $0<s<1<p$ and $sp<3$. Our goal is twofold. First, we define and study suitable functional settings for such operator proving…
The short note here is to give a few heuristic arguments on the weird looking fractional Laplacian operator. This is certainly going to expand the vision of a reader who is looking to develope a taste for research in this direction.
Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…
Leading idea of this manuscript is to discuss the structure and the deep correlations among different quantum physical systems, and to explore how such correlations bear on the capacity of the systems to encode and manipulate information.…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
This essay aims at emphasizing the potential of a synergy between quantum gravity and the quantum computing technologies. Such a combination would be beneficial for both understanding the Planck scale physics and the stimulation of…
In this paper we study strongly indefinite systems involving the fractional Laplacian on bounded domains. We obtain existence and non-existence results, $a priori$ estimates of Gidas-Spruck type, and the symmetric property.
We extend discrete calculus for arbitrary ($p$-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular…
We study quantum caustics in $d$-dimensional systems with quadratic Lagrangians. Based on Schulman's procedure in the path-integral we derive the transition amplitude on caustics in a closed form for generic multiplicity $f$, and thereby…
The aim of this paper is to bring together a new type of quantum calculus, namely $p $-calculus, and variational calculus. We develop $p $-variational calculus and obtain a necessary optimality condition of Euler-Lagrange type and a…
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent…
This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus…
Several approaches to the formulation of a fractional theory of calculus of "variable order" have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an…