We investigate variational methods for finding approximate solutions to the Fokker-Planck equation, especially in cases lacking detailed balance. These schemes fall into two classes: those in which a Hermitian operator is constructed from the (non-Hermitian) Fokker-Planck operator, and those which are based on soluble approximations to this operator. The various approaches are first tested on a...

Over the past few decades there has been an enormous growth in the numbers of papers devoted to experimental and theoretical aspects of anomalous diffusion [1, 2]. The landmark review by Metzler and Klafter in 2000 [1] has been particularly influential, promoting the description of anomalous diffusion within the framework of continuous time random walks (CTRWs) and fractional calculus. There ar...

*Correspondence: [email protected] Faculty of Computer Science and Information Technology, University Malaya, Kuala Lumpur, 50603, Malaysia Abstract Cloud computing is relevant for the applications transported as services over the hardware and for the Internet and systems software in the datacenters that deliver those services. The major problem for this state is computing the capacity and...

We present an analytic study for subdiffusive escape of overdamped particles out of a cusp-shaped parabolic potential well which are driven by thermal, fractional Gaussian noise with a 1/omega 1-alpha power spectrum. This long-standing challenge becomes mathematically tractable by use of a generalized Langevin dynamics via its corresponding non-Markovian, time-convolutionless master equation: W...

The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential V(x)=ax{2}/2+bx{4}/4 is considered. An exact solution of the fractional Klein-Kramers (Fokker-Planck) equation is obtained allowing one to calculate via matrix continued fractions the positional autocorrelation function and dynamic susceptibility describing the position ...