Existence and continuous dependence of mild solutions for fractional abstract differential equations with infinite delay
نویسندگان
چکیده
In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay. The results are obtained by using the Krasnoselskii’s fixed point theorem and the theory of resolvent operators for integral equations.
منابع مشابه
Existence and continuous dependence for fractional neutral functional differential equations
In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.
متن کاملTheory of Hybrid Fractional Differential Equations with Complex Order
We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...
متن کاملExistence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay
...
متن کامل$L^p$-existence of mild solutions of fractional differential equations in Banach space
We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.
متن کاملOn time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کامل