Discrete Mittag-Leffler functions in linear fractional difference equations

Abstract and Applied Analysis

Volumn 2011, Issue , 2011, Pages

  Čermák, Jan ^a   Kisela, Tomáš ^a   Nechvátal, Luděk ^a  

^a BRNO UNIVERSITY OF TECHNOLOGY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052649257     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2011/565067     Document Type: Article

References (20)

1. Agarwal R. P., Certain fractional q -integrals and q -derivatives Mathematical Proceedings of the Cambridge Philosophical Society 1969 66 365 370
2. Diaz J. B., Osler T. J., Differences of fractional order Mathematics of Computation 1974 28 185 202
3. Gray H. L., Zhang N. F., On a new definition of the fractional difference Mathematics of Computation 1988 50 182 513 529
4. Miller K. S., Ross B., Fractional difference calculus Univalent Functions, Fractional Calculus, and Their Applications (Koriyama, 1988) 1989 Chichester, UK Horwood 139 152 Ellis Horwood Series: Mathematics and Its Applications
5. Atici F. M., Eloe P. W., A transform method in discrete fractional calculus International Journal of Difference Equations 2007 2 2 165 176
6. Atici F. M., Eloe P. W., Fractional q -calculus on a time scale Journal of Nonlinear Mathematical Physics 2007 14 3 341 352
7. Čermák J., Nechvtal L., On (q, h) -analogue of fractional calculus Journal of Nonlinear Mathematical Physics 2010 17 1 51 68
8. Bohner M., Peterson A., Dynamic equations on time scales 2001 Boston, Mass, USA Birkhauser x+358
9. Bohner M., Peterso A., Advances in Dynamic Equations on Time Scales 2003 Boston, Mass, USA Birkhauser xii+348
10. Anastassiou G. A., Foundations of nabla fractional calculus on time scales and inequalities Computers Mathematics with Applications 2010 59 12 3750 3762
11. Andrews G. E., Askey R., Roy R., Special Functions 1999 71 Cambridge, UK Cambridge University Press xvi+664 Encyclopedia of Mathematics and Its Applications
12. Atici F. M., Eloe P. W., Initial value problems in discrete fractional calculus Proceedings of the American Mathematical Society 2009 137 3 981 989
13. Atici F. M., Eloe P. W., Discrete fractional calculus with the nabla operator Electronic Journal of Qualitative Theory of Differential Equations 2009 2009 2 12
14. Mansour Z. S. I., Linear sequential q -difference equations of fractional order Fractional Calculus Applied Analysis 2009 12 2 159 178
15. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering
16. Nagai A., On a certain fractional q -difference and its eigen function Journal of Nonlinear Mathematical Physics 2003 10 supplement 2 133 142
17. Čermák J., Kisela T., Note on a discretization of a linear fractional differential equation Mathematica Bohemica 2010 135 2 179 188
18. Kilbas A. A., Saigo M., Saxena R. K., Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the kernels Journal of Integral Equations and Applications 2002 14 4 377 396
19. Kilbas A. A., Saigo M., Saxena R. K., Generalized Mittag-Leffler function and generalized fractional calculus operators Integral Transforms and Special Functions 2004 15 1 31 49 (Pubitemid 38170026)
20. Atici F. M., Eloe P. W., Linear systems of fractional nabla difference equations Rocky Mountain Journal of Mathematics 2011 41 353 370