Overview of fractional h-difference operators

Operator Theory: Advances and Applications

Volumn 229, Issue , 2013, Pages 253-268

  Mozyrska, Dorota ^a   Girejko, Ewa ^a  

^a BIALYSTOK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Fractional derivative; Fractional difference equation; Fractional difference operator

Indexed keywords

EID: 85060035175     PISSN: 02550156     EISSN: 22964878     Source Type: Book Series    
DOI: 10.1007/978-3-0348-0516-2_14     Document Type: Article

References (23)

1. T. Abdeljawad, On Riemann and Caputo fractional differences. Comput. Math. Appl. 62 (3) (2011), 1602-1611
2. T. Abdeljawad, D. Baleanu, Fractional differences and integration by parts. J. Comput. Anal. Appl. 13 (3) (2011), 574-582
3. O.P. Agrawal, D. Baleanu. A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems. J. Vib. Control 13 (9-10) (2007), 1269-1281
4. G.A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph, Springer, New York 2009
5. F.M. Atici, P.W. Eloe, Initial value problems in discrete fractional calculus. Proc. Amer. Math. Soc. 137 (3) (2008), 981-989
6. F.M. Atici, P.W. Eloe, A Transform Method in Discrete Fractional Calculus. Int. J. Difference Equ. 2 (2007), 165-176
7. D. Baleanu, New applications of fractional variational principles. Rep. Math. Phys. 61 (2) (2008), 199-206
8. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Method. World Scientific Publishing, New York 2012
9. N.R.O. Bastos, R.A.C. Ferreira, D.F.M. Torres, Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete Contin. Dyn. Syst. 29 (2) (2011), 417-437
10. J. Čermák, T. Kisela, L. Nechvátal, Discrete Mittag-Leffler functions in linear fractional difference equations. Abst. Appl. Anal. (2011), 1-21
11. F. Chen, X. Luo, Y. Zhou, Existence results for nonlinear fractional difference equation. Advances in Difference Eq. article ID 713201, 12 p., doi: 10.1155/2011/7132012011
12. R.A.C. Ferreira, D.F.M. Torres, Fractional h-difference equations arising from the calculus of variations. Appl. Anal. Discrete Math. 5 (1) (2011), 110-121
13. M.T. Holm, The theory of discrete fractional calculus: Development and application. University of Nebraska - Lincoln 2011
14. T. Kaczorek, Positive 1D and 2D Systems Springer-Verlag, London 2002
15. J. Klamka, Controllability of nonlinear discrete systems. Int. J. Appl. Math. Comput. Sci. 12 (2) (2002), 173-180
16. K.S. Miller, B. Ross, Fractional difference calculus. Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and their Applications, Nihon University, Kōriyama, Japan (1989), 139-152
17. K.S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations Wiley, New York 1993
18. M.D. Ortigueira, Fractional central differences and derivatives. J. Vib. Control 14 (9-10) (2008), 1255-1266
19. P. Ostalczyk, The non-integer difference of the discrete time function and its application to the control system synthesis. Int. J. Syst. Sci. 31 (12) (2000), 1551-1561
20. I. Podlubny, Fractional Differential Equations. AP, New York, NY 1999
21. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and derivatives. Translated from the 1987 Russian original, Gordon and Breach, Yverdon 1993
22. D. Sierociuk, D. Dzielínski, Fractional Kalman filter algorithm for the states parameters and order of fractional system estimation. Int. J. Appl. Math. Comp. Sci. 16 (1) (2006), 129-140
23. M.F. Silva, J.A. Tenreiro Machado, R.S. Barbosa, Using fractional derivatives in joint control of hexapod robots. J. Vib. Control 14 (9-10) (2008), 1473-1485.