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Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives. (English) Zbl 1172.26307

By employing the method of monotone iteration, a result on the existence and uniqueness of a solution of the initial value problem for fractional differential equation

D α u(t)=f(t,u),t(0,T],t 1-α u(t) t=0 =u 0 ,

where 0<T<+ and D α is the Riemann-Liouville fractional derivative of order 0<α<1 is established and discussed.

MSC:
26A33Fractional derivatives and integrals (real functions)
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34A40Differential inequalities (ODE)
34A99General theory of ODE