The existence and uniqueness of solutions to the two-dimensional stochastic magneto-hydrodynamic system is established in the presence of either a multiplicative noise or an additive fractional Brownian noise. The method of monotonicity is employed when the noise is multiplicative. In the case of a fractional Brownian noise, a unique mild solution of the system is established under suitable con...

the main attempt of this article is extension the method so that it generallywould be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. there-fore we consider a control system governed by a bone marrow cancer equation.next, by extending the underlying space, the existence of the solution is con-sidered and ...

In this paper, we prove the existence and uniqueness of squaremean asymptotically almost automorphic mild solution of a class of partial nonlocal neutral stochastic functional integro-differential equations with resolvent operators in a real separable Hilbert space. An example illustrating our main result is given.

Abstract. In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory ...

In this work, we prove a result on the local existence of mild solution in the α-norm for some partial functional differential equations with infinite delay. We suppose that the linear part generates a compact analytic semigroup. The nonlinear part is just assumed to be continuous. We use the compactness method, to show the main result of this work. Some application is provided.

This paper is concerned with the controllability result of mild solution for an impulsive neutral fractional order stochastic integro-differential equation with infinite delay subject to nonlocal conditions. The existence result is obtained by using the fixed point technique on a Hilbert space. At last, we present an example to verify the result. MSC: 93B05 • 26A33 • 34K05 • 34A37 • 34K50

In this work, we prove results on the local existence of mild solution and global continuation in the α-norm for some class of partial neutral differential equations. We suppose that the linear part generates a compact analytic semigroup. The nonlinear part is just assumed to be continuous. We use the compactness method, to show the main result of this work.

By using the theory of semigroups of growth α, we prove the existence and uniqueness of the mild solution for the random impulsive functional differential equations involving almost sectorial operators. An example is given to illustrate the theory. c ©2012 NGA. All rights reserved.

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivar...