Browsing by Author "Wang, JinRong"

Now showing 1 - 12 of 12

Access status: Open Access ,
A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions
(2011) Wang, JinRong; Yan, X.; Zhang, X.-H.; Wang, T.-M.; Li, X.-Z.
In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type $\begin{aligned}D_{t}^{q}x(t)=Ax(t)+\int\limits_{0}^{t}B(t-s)x(s)ds+t^{n}f\left(t,x(t)\right),&\;t\in [0,T],\;n\in Z^{+},\\&q\in(0,1],\;x(0)=g(x)+x_{0}.\end{aligned}$ Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point theorems due to Banach's fixed point theorem, Krasnoselskii's fixed point theorem and Schaefer's fixed point theorem. At last, an example is given for demonstration.
Access status: Open Access ,
Analysis of integrodifferential control system with pulse-width modulated sampler on Banach spaces
(2012) Wang, JinRong
This paper studies steady-state control and stability for a class of integrodifferential control system with pulse-width modulated sampler on Banach spaces. The existence and stability of the steady-state for the integrodifferential control system with pulse-width modulated sampler are given. An example is given to illustrate the theory.
Access status: Open Access ,
Existence and stabilizability of steady-state for semilinear pulse-width sampler controlled system
(2011) Wang, JinRong
In this paper, we study the steady-state of a semilinear pulse-width sampler controlled system on infinite dimensional spaces. Firstly, by virtue of Schauder's fixed point theorem, the existence of periodic solutions is given. Secondly, utilizing a generalized Gronwall inequality given by us and the Banach fixed point theorem, the existence and stabilizability of a steady-state for the semilinear control system with pulse-width sampler is also obtained. At last, an example is given for demonstration.
Access status: Open Access ,
Existence and uniqueness results for fractional differential equations with boundary value condition
(2011) Lv, LinLi; Wang, JinRong; Wei, Wei
In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results.
Access status: Open Access ,
Existence results for mild solutions of impulsive periodic systems
(2012) Yang, YanLong; Wang, JinRong
By applying the Horn’s fixed point theorem, we prove the existence of $T_0$-periodic $PC$-mild solution of impulsive periodic systems when $PC$-mild solutions are ultimate bounded.
Access status: Open Access ,
Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control
(Wydawnictwa AGH, 2010) Wang, JinRong; Wei, W.; Yang, YanLong
In this paper, a class of fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is considered. Using a contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequality, the existence and uniqueness of mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is also presented.
Access status: Open Access ,
Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces
(2010) Wang, JinRong; Yang, YanLong; Wei, W.
In this paper, we study the existence and uniqueness of the $PC$-mild solution for a class of impulsive fractional differential equations with time-varying generating operators and nonlocal conditions. By means of the generalized Ascoli-Arzela Theorem given by us and the fixed point theorem, some existence and uniqueness results are obtained. Finally, an example is given to illustrate the theory.
Access status: Open Access ,
On controllability for fractional differential inclusions in Banach spaces
(2012) Wang, JinRong; Li, XueZhu; Wei, Wei
In this paper, we investigate the controllability for systems governed by fractional differential inclusions in Banach spaces. The techniques rely on fractional calculus, multivalue mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem.
Access status: Open Access ,
On nonlocal problems for fractional differential equations in Banach spaces
(2011) Dong, XiWang; Wang, JinRong; Zhou, Yong
In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Access status: Open Access ,
On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces
(2011) Yang, YanLong; Wang, JinRong
In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.
Access status: Open Access ,
On some impulsive fractional differential equations in Banach spaces
(2010) Wang, JinRong; Wei, W.; Yang, YanLong
This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of $PC$-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.
Access status: Open Access ,
On the stability of first order impulsive evolution equations
(2014) Wang, JinRong; Fečkan, Michal; Zhou, Yong
In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised. Ulam-Hyers-Rassias stability results on a compact interval and an unbounded interval are presented by using an impulsive integral inequality of the Gronwall type. Two examples are also provided to illustrate our results. Finally, some extensions of the Ulam-Hyers-Rassias stability for the case with infinite impulses are given.