TY - JOUR

T1 - The profile of blowing-up solutions to a nonlinear system of fractional differential equations

AU - Kirane, Mokhtar

AU - Malik, Salman A.

PY - 2010/12/15

Y1 - 2010/12/15

N2 - 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>1 are given constants and D0+α and D0+β, 0<α<1, 0<β<1, stand for the RiemannLiouville 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.

AB - 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>1 are given constants and D0+α and D0+β, 0<α<1, 0<β<1, stand for the RiemannLiouville 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.

KW - Blow-up time

KW - Fractional derivative

KW - Integral equations

KW - Laplace transform

KW - Nonlinear system

UR - http://www.scopus.com/inward/record.url?scp=77956899693&partnerID=8YFLogxK

U2 - 10.1016/j.na.2010.06.088

DO - 10.1016/j.na.2010.06.088

M3 - Article

AN - SCOPUS:77956899693

SN - 0362-546X

VL - 73

SP - 3723

EP - 3736

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -