Zhan-Dong Mei - School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China (email)
Abstract: 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.
Keywords: General fractional abstract Cauchy problem,
general Riemann-Liouville fractional derivative,
general fractional resolvent.
Received: October 2012; Revised: January 2013; Published: May 2013.
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