and Applied Analysis 3 The first variant of differential operator was used in 13 to study the existence of solutions x t of nonlinear fractional differential equations that obey the restrictions x t −→ 1 when t −→ ∞, x′ ∈ ( L1 ∩ L∞ ) 0, ∞ ,R . 1.5 The second variant of differential operator, see 14 , was employed to prove that, for any real numbers x0, x1, the linear fractional differential equ...

Given a sequence of i.i.d. random functions Ψn:R→R, n∈N, we consider the iterated function system and Markov chain, which is recursively defined by X0x:=x Xnx:=Ψn−1(Xn−1x) for x∈R n∈N. Under two basic assumptions that Ψn are a.s. continuous at any point in R asymptotically linear “endpoints” ±∞, study tail behavior stationary laws such chains means renewal theory. Our approach provides an exten...

This paper considers the problem of distributed adaptive linear parameter estimation in multiagent inference networks. Local sensing model information is only partially available at the agents, and interagent communication is assumed to be unpredictable. The paper develops a generic mixed time-scale stochastic procedure consisting of simultaneous distributed learning and estimation, in which th...

where Ω is a bounded domain in RN (N ≥ 1) with smooth boundary ∂Ω. The conditions imposed on f (x, t) are as follows: (f1) f ∈ C(Ω×R,R); f (x,0) = 0, for all x ∈Ω. (f2) lim|t|→0( f (x, t)/t) = μ, lim|t|→∞( f (x, t)/t) = uniformly in x ∈Ω. Since we assume (f2), problem (1.1) is called asymptotically linear at both zero and infinity. This kind of problems have captured great interest since the pi...