Abstract
In this paper, we are concerned with a class of abstract fractional relaxation equations. We develop a new notion, named fractional resolvent and derive some of its properties. By virtue of the obtained properties and the properties of general Mittag-Leffler function, we present some sufficient conditions to guarantee that the classical solutions of homogeneous and inhomogeneous fractional relaxation equations exist. An illustrative example is presented.
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Acknowledgements
The authors wish to thank the anonymous reviewers for helpful and insightful comments and suggestions.
Notes
This work was supported by the Natural Science Foundation of China [grant number 11301412] and [grant number 11131006]; Research Fund for the Doctoral Program of Higher Education of China [grant number 20130201120053]; Shaanxi Province Natural Science Foundation of China [grant number 2014JQ1017]; Project funded by China Postdoctoral Science Foundation [grant number 2014M550482], the Fundamental Research Funds for the Central Universities [grant number 2012jdhz52]. Part of this work was done during the first author was visiting Prof. Bao-Zhu Guo at Academy of Mathematics and Systems Science, The Chinese Academy of Sciences.