Danh Hua Quoc Nam, Tran Thanh Binh, and Nguyen Huu Can.

On a Fractional Parabolic Equation with Kirchhoff’s Type and Conformable Derivative. Dynamic Systems and Applications 30 (2021) No.1, 49-65

https://doi.org/10.46719/dsa20213014

ABSTRACT.
In this paper, we study a diffusion equation of  Kirchhoff-type  with conformable  fractional derivative. The global existence and uniqueness of mild solutions is established.  Some regularity results for the mild solution and its derivatives  are also derived. The main tool for analysis in this paper  is use Banach fixed point theory and Sobolev embeddings.  

AMS (MOS) Subject Classification. 35R11, 35B65, 26A33