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Nabla discrete fractional calculus and nabla inequalities. (English) Zbl 1190.26001

Summary: Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remainders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities.

MSC:

26A33 Fractional derivatives and integrals
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References:

[1] Atici, F.; Eloe, P., Discrete fractional calculus with the nabla operator, Electron. J. qual. theory differ. equ. spec. ed. I, 1, 1-99, (2009), http://www.math.u-szeged.hu/ejqtde/ · Zbl 1189.39004
[2] Anderson, D.R., Taylor polynomials for nabla dynamic equations on time scales, Panamer. math. J., 12, 4, 17-27, (2002) · Zbl 1026.34011
[3] Atici, F.; Eloe, P., Initial value problems in discrete fractional calculus, Proc. AMS, 137, 3, 981-989, (2009) · Zbl 1166.39005
[4] G. Anastassiou, Discrete fractional Calculus and inequalities, 2009 (submitted for publication)
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