Initial value problems in discrete fractional calculus

Proceedings of the American Mathematical Society

Volumn 137, Issue 3, 2009, Pages 981-989

  Atici, Ferhan M ^a   Eloe, Paul W ^b  

^a WESTERN KENTUCKY UNIVERSITY   (United States)

^b UNIVERSITY OF DAYTON   (United States)

Author keywords

Discrete fractional calculus

Indexed keywords

EID: 74149083825     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-08-09626-3     Document Type: Article

References (11)

1. F. M. ATICI AND P. W. ELOE, A transform method in discrete fractional calculus, International Journal of Difference Equations, Vol. 2, 2 (2007), pp. 165-176.
2. F. M. ATICI AND P. W. ELOE, Fractional q-calculus on a time scale, Journal of Nonlinear Mathematical Physics, Vol. 14, 3 (2007), pp. 333-344. MR2350094
3. M. BOHNER AND G. GUSEINOV, The convolution on time scales, Abstract and Applied Analysis, 2007, Art. ID 58373, 24 pp. MR2320804 (2008f:44001)
4. M. BOHNER AND A. PETERSON, Dynamic Equations on Time S'cales, Birkhäuser, Boston, 2001. MR1843232 (2002c:34002)
5. M. BOHNER AND A. PETERSON, Laplace transform and Z-transform: Unification and extension, Methods and Applications of Analysis, Vol. 9, 1 (2002), pp. 151-157. MR1948468 (2003m:34027) (Pubitemid 36260358)
6. W. G. KELLEY AND A. C. PETERSON, Difference Equations: An Introduction with Applications, Harcourt/Academic Press, San Diego, CA, 2001. MR1765695 (2001i:39001)
7. K. S. MILLER AND B. ROSS, Fractional Difference Calculus, Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications, Nihon University, Koriyama, Japan, May 1988, pp. 139-152;
8. Ellis Horwood Ser. Math. Appl., Horwood, Chichester, 1989. MR1199147 (93h:26010)
9. K. S. MILLER AND B. ROSS, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, Inc., New York, 1993. MR1219954 (94e:26013)
10. I. PODLUBNY, Fractional Differential Equations, Academic Press, San Diego, CA, 1999. MR1658022 (99m:26009)
11. S. G. SAMKO, A. A. KILBAS, AND O. I. MARICHEV, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993. MR1347689 (96d:26012)