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Zbl 1166.39005
Atici, Ferhan M.; Eloe, Paul W.
Initial value problems in discrete fractional calculus.
(English)
[J] Proc. Am. Math. Soc. 137, No. 3, 981-989 (2009). ISSN 0002-9939; ISSN 1088-6826/e

Authors' abstract: This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first carefully develop the commutativity properties of the fractional sum and the fractional difference operators. Then a $\nu$-th ($0<\nu \leq 1$) order fractional difference equation is defined. A nonlinear problem with an initial condition is solved and the corresponding linear problem with constant coefficients is solved as an example. Further, the half-order linear problem with constant coefficients is solved with a method of undetermined coefficients and with a transform method.
[Fozi Dannan (Damascus)]
MSC 2000:
*39A12 Discrete version of topics in analysis
26A33 Fractional derivatives and integrals (real functions)
39A20 Generalized difference equations
39A10 Difference equations

Keywords: discrete fractional calculus; fractional difference equations; commutativity; fractional sum; method of undetermined coefficients

Cited in: Zbl 1225.39008

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