an:06171071
Zbl 1273.34012
Mei, Zhan-Dong; Peng, Ji-Gen; Zhang, Yang
On general fractional abstract Cauchy problem
EN
Commun. Pure Appl. Anal. 12, No. 6, 2753-2772 (2013).
00318529
2013
j
34A08 47D06 34A12 34G20
general fractional abstract Cauchy problem; general Riemann-Liouville fractional derivative; general fractional resolvent
Summary: This paper is concerned with general fractional Cauchy problems of order \(0 < \alpha < 1\) and type \(0 \leq \beta \leq 1\) in infinite-dimensional Banach spaces. A new notion, named general fractional resolvent of order \(0 < \alpha < 1\) and type \(0 \leq \beta \leq 1\), is developed. Some of its properties are obtained. Moreover, some sufficient conditions are presented to guarantee that the mild solutions and strong solutions of homogeneous and inhomogeneous general fractional Cauchy problem exist. An illustrative example is presented.