## 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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### References:

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