References
- F.M.Atici and P.W.Eloe, Initial value problems in discrete fractional calculus, Proc. Am. Math. Soc.137(3) (2009), pp. 981–989. doi:10.1090/S0002-9939-08-09626-3.
- F.M.Atici and P.W.Eloe, Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory Differ. Equ.3 (2009), pp. 1–12.
- G.Anastassiou, Foundations of nabla fractional calculus on time scales and inequalities, Comput. Math. Appl.59(12) (2010), pp. 3750–3762. doi:10.1016/j.camwa.2010.03.072.
- J.Baoguo, L.Erbe and A.Peterson, Two monotonicity results for nabla and delta fractional differences, submitted for publication.
- M.Bohner and A.Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, MA, 2001.
- M.Bohner and A.Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, MA, 2003.
- R.Dahal and C.Goodrich, A monotonicity result for discrete fractional difference operators, Arch. Math.102(3) (2014), pp. 293–299. doi:10.1007/s00013-014-0620-x.
- Z.Denton and A.S.Vatsala, Fractional integral inequalities and applications, Comput. Math. Appl.59(3) (2010), pp. 1087–1094. doi:10.1016/j.camwa.2009.05.012.
- R.A.C.Ferreira, A discrete fractional Gronwall inequality, Proc. Am. Math. Soc.140(5) (2012), pp. 1605–1612. doi:10.1090/S0002-9939-2012-11533-3.
- C.Goodrich and A.Peterson, Discrete Fractional Calculus, Preliminary Version,2014.
- C.Goodrich, A convexity result for fractional differences, Appl. Math. Lett.35 (2014), pp. 58–62. doi:10.1016/j.aml.2014.04.013.
- W.Kelley and A.Peterson, Difference Equations: An Introduction with Applications, 2nd ed., Academic Press, Harcourt, 2001.
- M.Holm, The theory of discrete fractional calculus: Development and applications, Ph.D. diss.,University of Nebraska-Lincoln,2011.
- M.Holm, Sum and difference compositions in discrete fractional calculus, CUBO13(3) (2011), pp. 153–184. doi:10.4067/S0719-06462011000300009.