Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userVariational Approach for Fractional Partial Differential Equations
203
0
0.0
(
0
)
Authors
Guo-cheng Wu
Ask ChatGPT about the research
No Arabic abstract
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Sever
rate research
Read More
The method of characteristics has played a very important role in mathematical physics. Preciously, it was used to solve the initial value problem for partial differential equations of first order. In this paper, we propose a fractional method of characteristics and use it to solve some fractional partial differential equations.
In this paper we present the tanh method to obtain exact solutions to coupled MkDV system. This method may be applied to a variety of coupled systems of nonlinear ordinary and partial differential equations.
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a direct relation of irreversible processes to the entropy change. We show that the properties imply various entropy dissipation conditions for hyperbolic relaxation problems. As an application of the observation, we propose an approximation method to solve relaxation problems. Moreover, the observation is interpreted physically and verified with eight (sets of) systems from different fields.
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamics of solitons and their asymptotic stability. Results of numerical simulation are given. The obtained results allow us to formulate a new general conjecture on attractors of $G$ -invariant nonlinear Hamiltonian partial differential equations. This conjecture suggests a novel dynamical interpretation of basic quantum phenomena: Bohrs transitions between quantum stationary states, wave-particle duality and probabilistic interpretation.
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to overcome such shortcomings, a fractional variational iteration method is proposed. The Lagrange multipliers can be identified explicitly based on fractional variational theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
