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.


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|ISSN 1686-0209|