Gou Haide, Li Baolin
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070 P.R. China.
J Inequal Appl. 2017;2017(1):252. doi: 10.1186/s13660-017-1526-5. Epub 2017 Oct 10.
In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the studied problem was given based on an operator family generated by the operator pair [Formula: see text] and probability density function. Combining the techniques of fractional calculus, measure of noncompactness, and fixed point theorem with respect to -set-contractive, we obtain a new existence result of mild solutions. The results obtained improve and extend some related conclusions on this topic. At last, we present an application that illustrates the abstract results.
在本文中，我们利用希尔弗分数阶导数来处理一类具有时滞的非线性分数阶非自治发展方程，该导数推广了著名的黎曼 - 刘维尔分数阶导数。基于由算子对[公式：见原文]和概率密度函数生成的算子族，给出了所研究问题的温和解的定义。结合分数阶微积分技术、非紧性测度以及关于 - 集压缩的不动点定理，我们得到了温和解的一个新的存在性结果。所得到的结果改进并扩展了关于该主题的一些相关结论。最后，我们给出一个应用来说明这些抽象结果。
