Browsing by Subject "nonlocal conditions"

Now showing 1 - 4 of 4

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 ,
Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions
(2013) Ntouyas, Sotiris K.
This paper studies the boundary value problem of nonlinear fractional differential equations and inclusions of order $q \in (1,2]$ with nonlocal and integral boundary conditions. Some new existence and uniqueness results are obtained by using fixed point theorems.
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.