[1] C.S. Goodrich, A.C. Peterson, Discrete fractional calculus, Springer, New York, 2015.
[2] G.C. Wu, D. Baleanu, Discrete fractional logistic map and its chaos. Nonlinear Dyn. 75 (2014), 283-287.
[3] G.C. Wu, D. Baleanu, Chaos synchronization of the discrete fractional logistic map. Signal Process. 102 (2014), 96-99.
[4] F.M. Atici, P.W. Eloe, A transform method in discrete fractional calculus, Int. J. Differ. Equ. 2:2 (2007), 165-176.
[5] F.M. Atici, P.W. Eloe, Initial value problems in discrete fractional calculus, Proc. Amer. Math. Soc. 137:3 (2009), 981989.
[6] F.M. Atici, P.W. Eloe, Two-point boundary value problems for finite fractional difference equations, J. Difference. Equ. Appl. 17 (2011), 445-456.
[7] T. Abdeljawad, On Riemann and Caputo fractional differences. Comput. Math. Appl. 62:3 (2011), 1602-1611.
[8] T. Abdeljawad, Dual identities in fractional difference calculus within Riemann. Adv. Differ. Equ. 2013, 2013:36, 16 pages.
[9] T. Abdeljawad, On delta and nabla Caputo fractional differences and dual identities. Discrete. Dyn. Nat. Soc. 2013, 2013:Article ID 406910, 12 pages.
[10] T. Abdeljawad, D. Baleanu, Fractional differences and integration by parts. J. Comput. Anal. Appl. 13:3 (2011), 574-582.
[11] M. Holm, Sum and difference compositions in discrete fractional calculus, Cubo. 13:3 (2011), 153184.
[12] G. Anastassiou, Foundations of nabla fractional calculus on time scales and inequalities, Comput. Math. Appl. 59 (2010), 37503762.
[13] B. Jia, L. Erbe, A. Peterson, Two monotonicity results for nabla and delta fractional differences, Arch. Math. 104 (2015), 589-597.
[14] B. Jia, L. Erbe, A. Peterson, Convexity for nabla and delta fractional differences, J. Difference Equ. and Appl. 21 (2015), 360-373.
[15] J. Cerm´ak, T. Kisela, L. Nechv´atal, Stability and asymptotic properties of a linear fractional difference equation, Adv. Differ. Equ. 2012, 2012:122, 14 pages.
[16] F. Jarad, T. Abdeljawad, D. Baleanu, K. Bi¸cen, On the stability of some discrete fractional nonautonomous systems. Abstr. Appl. Anal. 2012, 2012: Article ID 476581, 9 pages.
[17] D. Mozyrska, M. Wyrwas, The Z-transform method and delta type fractional difference operators. Discrete Dyn. Nat. Soc. 2015, 2015:12, 12 pages.
[18] D. Mozyrska, M. Wyrwas, Explicit criteria for stability of fractional h-difference two-dimensional systems, Int. J. Dynam. Control 5 (2017), 49.
[19] R.A.C. Ferreira, D.F.M. Torres, Fractional h-difference equations arising from the calculus of variations, Appl. Anal. Discr. Math. 5:1 (2011), 110 121.
[20] R.A.C. Ferreira, Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one, J. Difference Equ. Appl. 19 (2013), 712-718.
[21] R.A.C. Ferreira, C.S. Goodrich, Positive solution for a discrete fractional periodic boundary value problem, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 19 (2012), 545557.
[22] C.S. Goodrich, Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions, Comput. Math. Appl. 61 (2011), 191-202.
[23] C.S. Goodrich,On a discrete fractional three-point boundary value problem, J. Difference. Equ. Appl. 18 (2012), 397-415.
[24] C.S. Goodrich, A convexity result for fractional differences, Appl. Math. Lett. 35 (2014), 5862.
[25] C.S. Goodrich, The relationship between sequential fractional difference and convexity. Appl. Anal. Discr. Math. 10:2 (2016), 345-365.
[26] R. Dahal, C.S. Goodrich, A monotonicity result for discrete fractional difference operators, Arch. Math. (Basel) 102:3 (2014), 293299.
[27] L. Erbe, C.S. Goodrich, B. Jia, A. Peterson, Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions, Adv. Differ. Equ. 2016, 2016:43. 31 pages.
[28] F. Chen, X.Luo, Y.Zhou, Existence results for nonlinear fractional difference equation, Adv. Differ. Equ. 2011, 2011: Article ID 713201, 12 pages.
[29] F. Chen, Y. Zhou, Existence and Ulam stability of solutions for discrete fractional boundary value problem, Discrete. Dyn. Nat. Soc. 2013, 2013: Article ID 459161, 7 pages.
[30] Y. Chen, X. Tang, Thee difference between a class of discrete fractional and integer order boundary value problems, Commun. Nonlinear Sci. 19 (12) (2014), 40574067.
[31] W. Lv, Solvability for discrete fractional boundary value problems with a plaplacian operator, Discrete. Dyn. Nat. Soc. 2013, 2013: Article ID 679290, 8 pages.
[32] W. Lv, Solvability for a discrete fractional three-point boundary value problem at resonance, Abstr. Appl. Anal. 2014, 2014: Article ID 601092, 7 pages.
[33] W. Lv, J. Feng, Nonlinear discrete fractional mixed type sum-difference equation boundary value problems in Banach spaces, Adv. Differ. Equ. 2014, 2014: article 184, 12 pages.
[34] H.Q. Chen, Y.Q. Cui, X.L. Zhao, Multiple solutions to fractional difference boundary value problems. Abstr. Appl. Anal. 2014, 2014: Article ID 879380, 6 pages.
[35] H.Q. Chen, Z. Jin, S.G. Kang, Existence of positive solutions for Caputo fractional difference equation. Adv. Differ. Equ. 2015, 2015:44, 12 pages.
[36] S.G. Kang, Y. Li, H.Q. Chen, Positive solutions to boundary value problems of fractional difference equations with nonlocal conditions. Adv. Differ. Equ. 2014, 2014:7, 12 pages.
[37] W. Dong, J. Xu, D.O. Regan, Solutions for a fractional difference boundary value problem. Adv. Differ. Equ. 2013, 2013:319, 12 pages.
[38] T. Sitthiwirattham, J. Tariboon, S.K. Ntouyas, Existence Results for fractional difference equations with three-point fractional sum boundary conditions. Discrete. Dyn. Nat. Soc. 2013, 2013:Article ID 104276, 9 pages.
[39] T. Sitthiwirattham, J. Tariboon, S.K. Ntouyas. Boundary value problems for fractional difference equations with three-point fractional sum boundary conditions. Adv. Differ. Equ. 2013, 2013:296, 13 pages.
[40] T. Sitthiwirattham, Existence and uniqueness of solutions of sequential nonlinear fractional difference equations with three-point fractional sum boundary conditions. Math. Method. Appl. Sci. 38 (2015), 2809-2815.
[41] T. Sitthiwirattham, Boundary value problem for p−Laplacian Caputo fractional difference equations with fractional sum boundary conditions. Math. Method. Appl. Sci. 39:6 (2016), 1522-1534.
[42] S. Chasreechai, C. Kiataramkul, T. Sitthiwirattham, On nonlinear fractional sum-difference equations via fractional sum boundary conditions involving different orders. Math. Probl. Eng. 2015, 2015:Article ID 519072, 9 pages.
[43] J. Reunsumrit, T. Sitthiwirattham, Positive solutions of three-point fractional sum boundary value problem for Caputo fractional difference equations via an argument with a shift. Positivity 20:4 (2016), 861-876.
[44] J. Reunsumrit, T. Sitthiwirattham, On positive solutions to fractional sum boundary value problems for nonlinear fractional difference equations. Math. Method. Appl. Sci. 39:10 (2016), 2737-2751.
[45] J. Soontharanon, N. Jasthitikulchai, T. Sitthiwirattham. Nonlocal Fractional Sum Boundary Value Problems for Mixed Types of Riemann-Liouville and Caputo Fractional Difference Equations. Dynam. Syst. Appl. 25 (2016), 409-414.
[46] S. Laoprasittichok, T. Sitthiwirattham. On a Fractional Difference-Sum Boundary Value Problems for Fractional Difference Equations Involving Sequential Fractional Differences via Different Orders. J. Comput. Aanal. Appl. 23:6 (2017), 1097-1111.
[47] B. Kaewwisetkul, T. Sitthiwirattham. On Nonlocal Fractional Sum-Difference Boundary Value Problems for Caputo Fractional Functional Difference Equations with Delay. Adv. Differ. Equ. 2017, 2017:219, 14 pages.
[48] Y. Pan, Z. Han, S. Sun, Y. Zhao, The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems. Abstr. Appl. Anal. 2012, 2012:Article ID 707631, 15 pages.
[49] C.S. Goodrich, Existence of a positive solution to a system of discrete fractional boundary value problems. Appl. Math. Comput. 217:9 (2011), 4740-4753.
[50] R. Dahal, D. Duncan, C.S. Goodrich, Systems of semipositone discrete fractional boundary value problems. J. Differ. Equ. Appl. 20:3 (2014), 473-491.
[51] C.S. Goodrich, Systems of discrete fractional boundary value problems with nonlinearities satisfying no growth conditions. J. Differ. Equ. Appl. 21:5 (2015), 437-453.
[52] C.S. Goodrich, Coupled systems of boundary value problems with nonlocal boundary conditions, Appl. Math. Lett. 41 (2015), pp. 1722.
[53] D.H. Griffel, Applied functional analysis. Ellis Horwood Publishers, Chichester, 1981.