期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 59, 期 11, 页码 3489-3499出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.03.040
关键词
Discrete fractional calculus; Initial value problem; Discrete Gronwall inequality; Continuity with respect to initial conditions
In this paper, we consider a fractional initial value problem (IVP) in the case where the order v of the fractional difference satisfies 0 < v <= 1. We show that solutions of this IVP satisfy a continuity condition both with respect to the order of the difference, v, 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. (C) 2010 Elsevier Ltd. All rights reserved.
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