Initial value problems in discrete fractional calculus. (English) Zbl 1166.39005

Atici, Ferhan M.; Eloe, Paul W.

Proc. Am. Math. Soc. 137, No. 3, 981-989 (2009).

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.

Reviewer: Fozi Dannan (Damascus)

MSC:

39A12	Discrete version of topics in analysis
26A33	Fractional derivatives and integrals
39A20	Multiplicative and other generalized difference equations
39A10	Additive difference equations

Keywords:

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

References:

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