Abstract
Abstract Using the techniques of approximate solutions, the analytic resolvent method, and the uniform continuity of the resolvent, we discuss the existence of mild solutions for nonlocal fractional differential equations governed by a linear closed operator which generates a resolvent. An example is also given to illustrate the application of our theory. MSC:34K37, 47A10.
Highlights
1 Introduction In this paper, we are concerned with the existence of mild solutions for the following fractional differential equation: Dαu(t) = Au(t) + Jt –αf t, u(t), t ∈ J = [, b], ( . )
We remark that the main difficulty in dealing with the nonlocal problem is how to get the compactness of the solution operator at zero
We study the existence of the nonlocal fractional differential equation ( . ) governed by operator A generating an analytic resolvent
Summary
1 Introduction In this paper, we are concerned with the existence of mild solutions for the following fractional differential equation: Dαu(t) = Au(t) + Jt –αf t, u(t) , t ∈ J = [ , b], We remark that the main difficulty in dealing with the nonlocal problem is how to get the compactness of the solution operator at zero. To get rid of these restrictive conditions, based on the works of Fan and Li [ ] and Zhu and Li [ ], we mainly apply the techniques of approximate solutions, the analytic resolvent method and the uniform continuity of the resolvent to get the mild solution of the nonlocal fractional differential equation
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