Related papers: Nonlinear reaction with fractional dynamics
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
"Synchronization of two dynamical systems" is the term used to describe the phenomenon when two or more systems gradually change their states or behaviors to become similar or identical. This can happen in a lot of fields, such as physics,…
In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be…
Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…
We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time…
This paper deals with feedback control of fractional-order Chua's system. The fractional-order Chua's system with total order less than three which exhibit chaos as well as other nonlinear behavior and theory for control of chaotic systems…
We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
In this paper, we study the following nonlinear Dirac-Bopp-Podolsky system \begin{equation*} \left\lbrace \begin{array}{rll} \displaystyle{ -i\sum_{k=1}^{3}\alpha_{k}\partial_{k}u+[V(x)+q]\beta u+wu-\phi u}&=f(x,u), \ \ &\text{in}\…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are…
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable…