Ho Duy Binh. Continuity of a Semi-Linear Fractional Reaction-Diffusion Equation System with Non-Local Conditions Regarding Fractional Order of the Time. Dynamic Systems and Applications 30 (2021) No.3, 371-398

https://doi.org/10.46719/dsa20213035

ABSTRACT.
In this article, the time fractional derivative is taken in the sense of Riemann- Liouville type. We give representation of solutions under Fourier series and analyze initial value problems for semi-linear fractional diffusion equation method. Then, we also research the stability of the fractional derivative order for the time under some assumptions on the input data. Our key idea is to combine the theories Mittag-Leffler functions, Banach fixed point theorem.

Keywords and phrase: Initial value problem, Riemann-Liouville derivative, the semi-linear fractional diffusion equation with memory term, continuity, fixed point theory.

AMS (MOS) Subject Classification. 39A10.