In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the firstor second-order time derivative by the Caputo fractional derivative Dt , α > 0; and the Laplacian operator by the fractional Laplacian (−∆) , β ∈ (0, 2]. We discuss and derive the analytical solutions...

We study the nonlinear eigenvalue problem−div(a(|∇u|)∇u) = λ|u|q(x)−2u in Ω, u = 0 on ∂Ω, where Ω is a bounded open set in R with smooth boundary, q is a continuous function, and a is a nonhomogeneous potential. We establish sufficient conditions on a and q such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational ar...

In this paper, sufficient conditions are given for the existence of limiting distribution of a nonhomogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q = (Qt )t 0 is absolutely continuous with respect to the distribution of ergodic random process Q◦ = (Q◦t )t 0, then Qt law −→ t→∞ wh...

In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X (t), t ≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration of the BDP). We find conditions of ex...

This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the microscopic variations over a much larger physical domain of interest. The heterogeneous multiscale method (HMM) is an efficient framework to approximate the soluti...

* Correspondence: [email protected] Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract In this paper, we are to establish a class of strong deviation theorems for the random fields relative to mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree. As corollaries, we obtain the st...

Suppose one can observe a Gaussian nonhomogeneous process with a continuous time parameter. At an unknown time the observed process may leave its standard state, the drift of the process changes and becomes equal to a nonrandom function. Subject to a restriction on the rate of false alarms, one wants to detect the change \as soon as possible". We investigate Page's and Shiryaev's sequential det...

The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation f x g x ∫∞ 0 k x − t f t dt ∫0 −∞ T x − t f t dt, where K, T are n × n matrix valued functions, n ≥ 1, with nonnegative integrable elements, are considered in one semiconservative singular case, where the matrix A ∫∞ −∞ K x dx is stochastic one and the matrix B ∫∞ −∞ T x dx is substochasti...

A software reliability growth model is one of the fundamental technique to assess software reliability quantitatively. The software reliability growth model is required to have a good performance in terms of goodness-of-fit, predictability, and so forth. In this paper, we propose dis-cretized software reliability growth models. As to the software reliability growth modeling, discretized nonhomo...

In this paper, we investigate the iterated order of solutions of homogeneous and nonhomogeneous linear differential equations where the coefficients are entire functions and satisfy certain growth conditions.