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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
45J05 Integro-ordinary differential equations
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