Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary optimality conditions of a reaction-diffusion SIR model with
  ABC fractional derivatives   The main aim of the present work is to study and analyze a reaction-diffusion
fractional version of the SIR epidemic mathematical model by means of the
non-local and non-singular ABC fractional derivative operator with complete
memory effects. Existence and uniqueness of solution for the proposed
fractional model is proved. Existence of an optimal control is also
established. Then, necessary optimality conditions are derived. As a
consequence, a characterization of the optimal control is given. Lastly,
numerical results are given with the aim to show the effectiveness of the
proposed control strategy, which provides significant results using the AB
fractional derivative operator in the Caputo sense, comparing it with the
classical integer one. The results show the importance of choosing very well
the fractional characterization of the order of the operators.

36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph