We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical pr...

Recently, the subject of fractional differential equations has emerged as an important area of investigation. Indeed, we can find numerous applications in viscoelasticity, electrochemistry, control, electromagnetic, porous media, and so forth. In consequence, the subject of fractional differential equations is gaining much importance and attention. For some recent developments on the subject, s...

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong. keywords fluctuation-dissipation theorem, Langevin equation, multiplicative noise, Levy flight.

Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such models have been particularly successful in computational cell biology, and in this case, the interactions are typically first-order. The Chemical Langevin Equation is a stochastic differential equation that can be regarded as an approximation to the underl...