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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
\[ D^{\alpha}u(t)= f(t,u), \quad t\in (0,T], \qquad t^{1-\alpha}u(t)\mid_{t=0} = u_ 0, \] where \(0<T<+\infty\) and \(D^{\alpha}\) is the Riemann-Liouville fractional derivative of order \(0<\alpha<1\) is established and discussed.

MSC:
26A33 Fractional derivatives and integrals
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
34A99 General theory for ordinary differential equations
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