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

We investigate the profile of the blowing-up solutions to the nonlinear nonlocal system (FDS): View the MathML sourceu′(t)+D0+α(u−u0)(t)=|v(t)|q,t>0, Turn MathJax on View the MathML sourcev′(t)+D0+β(v−v0)(t)=|u(t)|p,t>0, Turn MathJax on 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 View the MathML sourceD0+α and View the MathML sourceD0+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.