The profile of blowing-up solutions to a nonlinear system of fractional differential equations

We investigate the profile of the blowing-up solutions to the nonlinear nonlocal system (FDS): u′(t)+D0+α(u−u0)(t)=|v(t)|q,t>0,v′(t)+D0+β(v−v0)(t)=|u(t)|p,t>0, where u(0)=u0>0,v(0)=v0>0,p>1,q>1u(0)=u0>0,v(0)=v0>0,p>1,q>1 are given constants and D0+α and D0+β, 0<α<10<α<1, 0<β<10<β<1, stand for the Riemann–Liouville fractional derivatives. Our method of proof relies on comparisons of the solution to the system (FDS) with solutions of the subsystems obtained from the system (FDS) by dropping either the usual derivatives or the fractional derivatives.