Nguyen Duc Phuong, Nguyen Anh Tuan, Tran Thanh Binh, and Tran Ngoc Thach.

On Time Fractional Diffusion Equation with Memory Term. Dynamic Systems and Applications 30 (2021) No.1, 67-78

https://doi.org/10.46719/dsa20213015

ABSTRACT.
In this paper,  we consider the existence results for time fractional diffusion equation with memory term. The time fractional derivative is taken in the sense of Riemann – Liouville type.  We also give  representation of solutions under Fouries series and we further establish the existence and uniqueness of the mild solution. In order to give the proof of the existence for mild solution, we have to find some suitable spaces.   Our main analysis for the study here  is of applying  Banach fixed point theorem and using some Sobolev embeddings.  

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