Abstract
This paper deals with the existence and uniqueness of mild solutions for a class of fractional evolution equations with nonlocal initial conditions. We present some local growth conditions on a nonlinear part and a nonlocal term to guarantee the existence theorems. An example is given to illustrate the applicability of our results.MSC: 34A12, 35F25.
Highlights
The differential equations involving fractional derivatives in time have recently been proved to be valuable tools in the modeling of many phenomena in various fields of engineering and science
The research on fractional differential equations has become an object of extensive study during recent years; see [ – ] and references therein
As remarked by Byszewski and Lakshmikantham, the nonlocal initial value problems can be more useful than the standard initial value problems to describe many physical phenomena
Summary
The differential equations involving fractional derivatives in time have recently been proved to be valuable tools in the modeling of many phenomena in various fields of engineering and science. Consider the existence and uniqueness of mild solutions of fractional evolution equation with nonlocal condition in the form
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