Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 110, pp. 1-28.

Title: Existence of global solutions and blow-up of solutions for coupled systems 
       of fractional diffusion equations
       
Authors: Bashir Ahmad  (King Abdulaziz Univ., Jeddah, Saudi Arabia)
         Ahmed Alsaedi (King Abdulaziz Univ., Jeddah, Saudi Arabia)
         Mohamed Berbiche (Mohamed Khider Univ., Biskra, Algeria)
         Mokhtar Kirane (Khalifa Univ. of Science, Abu Dhabi, United Arab Emirates)

Abstract:
 We study the Cauchy problem for a system of semi-linear coupled
 fractional-diffusion equations with polynomial nonlinearities posed in
 $\mathbb{R}_{+}\times \mathbb{R}^N$. Under appropriate conditions on the
 exponents and the orders of the fractional time derivatives, we present a
 critical value of the dimension N, for which global solutions with small
 data exist, otherwise solutions blow-up in finite time. Furthermore, the
 large time behavior of global solutions is discussed.
 
Submitted May 1, 2019. Published November 02, 2020.
Math Subject Classifications: 35A01, 35R09, 35K10, 45K05.
Key Words: Coupled fractional-diffusion equations;  polynomial nonlinearities;
           global solution; blow-up.