Related papers: A Hopf type lemma for fractional equations
This paper deals with a semi-classical limit (Theorem 1) by using traditional mathematical methods, and shows a Hopf theorem as a corollary. A formal discussion of it may be found in [7].
This paper is concerned with the qualitative properties of the solutions of mixed integro-differential equation \begin{equation}\label{eq 1} \left\{ \arraycolsep=1pt \begin{array}{lll} (-\Delta)_x^{\alpha} u+(-\Delta)_y u+u=f(u)\quad \ \…
Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions. This allows…
We settle an old question about the existence of certain "sums-of-squares" formulas over a field F (which are the simplest examples of composition formulas for quadratic forms). A classical theorem says that if such a formula exists over a…
A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a…
In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An…
In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators.…
We prove a representation formula of intrinsic Hopf-Lax type for subsolutions to Hamilton-Jacobi equations involving a Caputo time-fractional derivative.
In this article we introduce an analytical method, namely Homotopy Analysis Transform Method (HATM) which is a combination of Homotopy Analysis Method (HAM) and Laplace Decomposition Method (LDM).This scheme is simple to apply linear and…
An algorithm is presented here, for discovering Hopf-Bifurcation varieties of polynomial dynamical systems. It is based on the expression of specific polynomials, as sums of products of first degree polynomials, with parametrical…
This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the…
In this article we study different extensions of the celebrated Hopf's boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
We establish, for the first time, a Zaremba-Hopf-Oleinik type boundary point lemma for uniformly elliptic partial differential equations in double divergence form, also known as stationary Fokker-Planck-Kolmogorov equations. As an…
In this work, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for solutions to fractional $p$-Laplacian equations. Then, the isolation of the first $(s,p)$-eigenvalue is shown in bounded open sets satisfying…
We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves a classical result by Crandall and Rabinowitz in the case where basic spaces are Hilbert spaces. Actually, our theorem does not need any…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…