We introduce a novel global Markov transition constraint (Mtc) to model finite state homogeneous Markov chains. We present two algorithms to filter the variable domains representing the imprecise probability distributions over the state space of the chain. The first filtering algorithm is based on the fractional knapsack problem and the second filtering algorithm is based on linear programming....

We develop the ltering theory in the case where both the signal and the observation are solutions of some stochastic diierential equation driven by a multiidimensional fractional Brownian motion. We show that the classical approach fails to give a closed equation for the lter and we develop another approach using an auxiliary processsvalued semimartingale which solves theoretically this problem...

We get fractional symmetric Fokker Planck and Einstein Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equations of the Brownian motion theory and contain symmetric fractional derivatives over velocity and space, respectively. With the help of these equation...

The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order β ∈ (0, 1) . The fundamental solution for the Cauchy problem is interpreted as a probability density of a selfsimilar non-Markovian stochastic process related to a phenomenon of subdiffusion (the variance grows in time sub-lin...

[1] In this study we incorporate the existing concept of fractional mobility into a stochastic framework for modeling the partial transport of mixed-size sediment. The model predicts the fractional transport rates with parameters such as the long-run moving probability, mean particle velocity, and fractional mobility, all varying with the dimensionless effective shear stress. Movement of bed lo...

Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributedorder time and Riesz space fractional convection-diffusion and Schrödinger type equations. We prove stability and optimal order of convergence O(h + (∆t) θ 2 + θ) for the distr...

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NR...

In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential Equations into nonlinear ordinary differential Equations. Afterwards, the (Gʹ/G)-expansion method has been implemented, to celeb...