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We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Previous attempts to analyse when these are minima ex- ist, but mainly…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a 1D harmonic potential. At the boundaries both the wave function and its first derivative are continuous and…
Based on recent developments in the theory of fractional Sobolev spaces, an interesting new class of nonlocal variational problems has emerged in the literature. These problems, which are the focus of this work, involve integral functionals…
We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have…
As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
We establish general assumptions under which a constrained vari- ational problem involving the fractional gradient and a local nonlin- earity admits minimizers.
We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator…
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…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
By means of variational methods we investigate existence, non-existence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical…
This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schr\"odinger-Poisson systems involving fractional Laplacian operator: \begin{equation}\label{eq*} \left\{ \aligned &(-\Delta)^{s} u+V(x)u+ \phi…
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…