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In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
Starting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
Recently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in  was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see ) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular (,Theorem 32). However, the counterexample does not explain why and where the proof given in  does not work. In this paper, we make a detailed analysis...
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