Related papers: Fedosov Quantization of Fractional Lagrange Spaces
In the present work, by taking advantage of a so-called practical limitation of fractional derivatives, namely, the absence of a simple chain and Leibniz's rules, we proposed a generalized fractional calculus of variation where the…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case…
The present article deals with the similarity method to tackle the fractional Schrodinger equation where the derivative is defined in the Riesz sense. Moreover the procedure of reducing a fractional partial differential equation (FPDE) into…
We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…
We extend Lyapunov--type Mittag--Leffler stability analysis for fuzzy nonlinear fractional differential equations (Caputo sense) and introduce a family of stronger, broadly applicable stability results. In particular, we develop (i) uniform…
The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…
In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some…
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…
We investigate here all the possible invariant metric functions under the action of various kinds of semi-direct product Poincar\'e subgroups and their deformed partners. The investigation exhausts the possible theoretical frameworks for…
Using Caputo fractional derivative of order $\alpha $ we build the fractional jet bundle of order $\alpha $ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
We extend the notion of convexity of functions defined on global nonpositive curvature spaces by introducing (geodesically) $h$-convex functions. We prove estimates of Hermite-Hadamard type via Katugampola's fractional integrals. We obtain…
In this paper, we propose a new model of fractional mimetic dark matter based on the fractional action-like variational approach FALVA implementation of fractionality. The model is non-local at classical level and its equations of motion…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the…
Let $L=-\operatorname{div}_x(A(x)\nabla_x)$ be a uniformly elliptic operator in divergence form in a bounded domain $\Omega$. We consider the fractional nonlocal equations $$\begin{cases} L^su=f,&\hbox{in}~\Omega,\\…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
In this paper we present a method to solve initial value problems for fractional growth models, such as generalizations of the exponential and logistic with periodic harvesting models. Using a discretization of the Caputo derivative we…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…