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Continuity of solutions to discrete fractional initial value problems. (English) Zbl 1197.39002
Summary: We consider a fractional initial value problem (IVP) in the case where the order $\nu$ of the fractional difference satisfies $0<\nu \leq 1$. We show that solutions of this IVP satisfy a continuity condition both with respect to the order of the difference, $\nu$, and with respect to the initial conditions, and we deduce several important corollaries from this theorem. Thus, we address a complication that arises in the fractional case but not in the classical (integer-order) case.

##### MSC:
 39A10 Additive difference equations 26A33 Fractional derivatives and integrals (real functions) 45J05 Integro-ordinary differential equations
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##### References:
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