The existence and uniqueness of a class of fractional differential equations

Abstract

By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, D0+qx(t)=f(t,x(t), D0+q-1x(t)), tε(0,T), x(0)=0, D0+q-1x(0)= x0, are discussed, where fεC([0,T]×ℝ2, ℝ),D0+qx(t) is the standard Riemann-Liouville fractional derivative, 1