Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate controllability for fractional diffusion equations by
  Dirichlet boundary control   In this paper, we consider the approximate controllability of partial
differential equations with time derivatives of non-integer order via boundary
control. We first show the unique existence of the solution under smooth
boundary conditions using the eigenfunction expansion. Next we also study the
dual system and apply their results to prove (i) the regularity of the solution
with non-smooth boundary conditions and (ii) approximate controllability.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th