Pseudo Almost Automorphic Solution of Semilinear Fractional Differential Equations with the Caputo Derivatives
Pseudo Almost Automorphic Solution of Semilinear Fractional Differential Equations with the Caputo Derivatives
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DOI：
10.1515/fca-2015-0056
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发表时间：
2015
影响因子：
3
通讯作者：
Dingjiang Wang;Zhinan Xia
中科院分区：
文献类型：
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作者：
Dingjiang Wang;Zhinan Xia
本文研究了一类含Caputo导数的半线性分数阶微分方程的（μ，ν）-伪几乎自守温和（经典）解的存在唯一性.主要结果是利用不动点理论、Leray-Schauder择一定理和算子的分数幂得到的。并给出了该方法在具有扩散的分数阶捕食系统中的应用。
Abstract In this paper, we deal with existence and uniqueness of (μ, ν)-pseudo almost automorphic mild (classical) solution to semilinear fractional differential equations with the Caputo derivatives. The main results are obtained by means of the fixed point theory, Leray-Schauder alternative theorem and fractional powers of operators. Moreover, an application to fractional predator-prey system with diffusion is given.