Existence of Mild Solutions for Nonlocal Semilinear Fractional Evolution Equations
نویسنده
چکیده
In this paper, we investigate a class of semilinear fractional evolution equations with nonlocal initial conditions given by (1) ⎧⎨ ⎩ dqu(t) dtq = Au(t)+(Fu)(t), t ∈ I, u(0)+g(u) = u0, where 0 < q< 1 , I is a compact interval. Sufficient conditions for the existence of mild solutions for the equation (1) are derived. The main tools include Laplace transform, Arzela-Ascoli’s Theorem, Schauder’s fixed point theorem and Operator theorem.
منابع مشابه
$L^p$-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.
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