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Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

Academic Editor: Patricia J. Y. Wong Copyright © 2018 Junfei Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use

Nonlocal fractional functional differential equations with measure of noncompactness in Banach space

with the nonlocal initial value problem Daxt Axt f t; xt; xt; t 2 0; T ; x0 / gx; where A is the infinitesimal generator of a strongly & Junfei Cao continuous semigroup of bounded linear operators

Weighted Stepanov-like pseudo-almost automorphic mild solutions for semilinear fractional differential equations

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D t α x ( t ) = A x ( t ) + D t α − 1 F ( t , x ( t ) ) , t ∈ R , where 1 < α < 2 , A is a linear densely defined operator of sectorial type of ω < 0 on a complex Banach space X and F is an...

Hilbert-type and Hardy-type integral inequalities with operator expressions and the best constants in the whole plane

By introducing a mixed kernel function and the proper parameters, a new Hilbert-type integral inequality with a best constant factor in the whole plane is derived. As an application, the operator expressions, reverse inequalities, and Hardy-type inequalities are considered.

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient : , where is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system...

On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

, Guangzhou 510310, China Received 20 December 2012; Accepted 20 February 2013 Academic Editor: Sotiris Ntouyas Copyright © 2013 Xianyong Huang and Junfei Cao. This is an open access article distributed

On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

, Guangzhou 510310, China Received 20 December 2012; Accepted 20 February 2013 Academic Editor: Sotiris Ntouyas Copyright © 2013 Xianyong Huang and Junfei Cao. This is an open access article distributed

Dynamics of stochastic Lorenz family of chaotic systems with jump

Zaitang Huang 0 Junfei Cao 0 Ting Jiang 0 0 J. Cao Department of Mathematics, Guangdong University of Education , Guangzhou 510310, People's Republic of China This paper discusses the Lorenz family

Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations

Received 2 August 2013; Accepted 21 August 2013 Academic Editors: K. Ammari and S. Kim Copyright © 2013 Junfei Cao et al. This is an open access article distributed under the Creative Commons Attribution