Some Uniqueness Results for Fractional Differential Equation of Arbitrary Order with Nagumo Like Conditions

Abdourazek Souahi, Assia Guezane-Lakoud, Amara Hitta

Abstract

In this work, we generalize the Krasnoselskii-Krein type of uniqueness theorem to $q>1$ arbitrary along with Kooi and Rogers ones.  The initial value problem is of the Riemann-Liouville type fractional differential equation, where the nonlinearity is depending on $D^{q-1}x$. Further, we establish the convergence of successive approximations of the Picard iterations of the equivalent Volterra integral equation. Finally, we give a numerical example illustrating the convergence of the successive approximations to the unique solution.