Default probability distributions are often defined in terms of their conditional default probability distribution, or their hazard rate. By their definition, they imply a unique probability density function. The applications of default probability distributions are varied, including the risk premium model used to price default bonds, reliability measurement models, insurance, etc. Fractional p...

We study, both analytically and by numerical modeling the equilibrium probability density function for an non-linear Lévy oscillator with the Lévy index α, 1 ≤ α ≤ 2, and the potential energy x 4. In particular, we show that the equilibrium PDF is bimodal and has power law asymptotics with the exponent −(α + 3). 1 Starting equations Recently, kinetic equations with fractional derivatives have a...

We discuss construction and applications of instanton-like objects which we call fractional space-like branes. These objects are localised at a fixed point of a time-like (or more generally space-time) orbifold which is a string theoretical toy model of a cosmological singularity. We formulate them in boundary state, adsorption, and fermionisation approaches. 1 Fractional space-like branes in a...

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

There are various fractional order systems existing. This paper deals with the modelling of fractional order systems using an old and unique model structure i.e. state space model. The fractional order process system can be mathematically modelled by state space model. Simulation results validated that the fractional order model using state space is better as compared to other models such as fi...

The exp((−φ(ξ))-expansion method is used as the first time to investigate the wave solution of a nonlinear the space-time nonlinear fractional PKP equation, the space-time nonlinear fractional SRLW equation, the space-time nonlinear fractional STO equation and the space-time nonlinear fractional KPP equation. The proposed method also can be used for many other nonlinear evolution equations.

The exp((-?(?))-expansion method is used as the first time to investigate the wave solution of a nonlinear the space-time nonlinear fractional PKP equation, the space-time nonlinear fractional SRLW equation, the space-time nonlinear fractional STO equation and the space-time nonlinear fractional KPP equation. The proposed method also can be used for many other nonlinear evolution equations.

We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri ...

The class of fractional linear generating functions, one of the few known classes of probability generating functions whose iterates can be explicitly stated, is examined. The method of bounding a probability generating function g (satisfying g"(1)< oo) by two fractional linear generating functions is used to derive bounds for the extinction time distribution of the Galton-Watson branching proc...

Previous work [51] showed how to solve time-fractional diffusion equations by particle tracking. This paper extends the method to the case where the order of the fractional time derivative is greater than one. A subordination approach treats the fractional time derivative as a random time change of the corresponding Cauchy problem, with a first derivative in time. One novel feature of the time ...