Related papers: Time fractional equations and probabilistic repres…

In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…

In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…

It is well-known that compositions of Markov processes with inverse subordinators are governed by integro-differential equations of generalized fractional type. This kind of processes are of wide interest in statistical physics as they are…

In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of…

In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…

We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…

A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original…

This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…

In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…

The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and…

We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide a stochastic representation of the solution and show that it…

We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to…

We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…

We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…

We study a nonlocal nonlinear parabolic problem with a fractional time derivative. We prove a Krylov-Safonov type result; mainly, we prove Holder regularity of solutions. Our estimates remain uniform as the order of the fractional time…

In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…