The aim of the present paper is to establish the existence, uniqueness and boundedness of solutions to the nonlocal fractional integrodifferential equations in Banach spaces. Mathematics Subject Classification: 26A33, 34K12, 34A40, 35B60, 45N05, 45G15

We consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. Various notions of weak solution are considered and compared. We establish existence and regularity results. In particular we study the boundedness of weak solutions. We also establish an existence result for a classical solution.

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.

In this paper we study the problem of deciding boundedness of (recursive) regular path queries over views in data integration systems, that is, whether a query can be re-expressed without recursion. This problem becomes challenging when the views contain recursion, thereby potentially making recursion in the query uncessary. We define and solve two related problems of boundedness of regular pat...

We present a finite element scheme capable of preserving the nonnegative and bounded solutions of the generalized Burgers-Huxley equation. Proofs of existence and uniqueness of a solution to the continuous problem together with some results concerning the boundedness and the nonnegativity of the solution are given. Under appropriate conditions on the mesh and the initial and boundary data, boun...

In this paper, dynamic behavior of a class of high-order fuzzy cellular neural networks (HFCNNs) with time-varying delays is investigated. Compared with the previous results in the literature, the restrictions are loosed, since we do not assume the boundedness and monotonicity on the activation functions, and the differentiability of time-varying delay functions. Some sufficient conditions are ...

This note establishes stationarity of a number of stochastic processes of interest in the study of Transport Protocols. For many of the processes studied in this note stationarity had been established before, but for one class the result is new. For that class, it was counterintuitive that stationarity was hard to prove. This note also explains why that class offered such stiff resistance. The ...