The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
On Riemann and Caputo fractional differences
Open accessAbstract
In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B., Atici F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions.
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Cites
Fractional Differential Equations
(2025) · MDPI eBooks · doi:10.3390/books978-3-7258-4742-6 · Cited by 20,278
Fractional Integrals and Derivatives, Theory and Applications
Samko, S. G., Kilbas, A. A., & Marichev, O. I. (1987) · CERN Document Server (European Organization for Nuclear Research) · Cited by 7,769
Fractional Calculus in Bioengineering
West, B. J. (2007) · Journal of Statistical Physics · doi:10.1007/s10955-007-9294-0 · Cited by 1,979
Hamiltonian Chaos and Fractional Dynamics
Zaslavsky, G. M. (2004) · doi:10.1093/oso/9780198526049.001.0001 · Cited by 726
Algorithms for the fractional calculus: A selection of numerical methods
Diethelm, K., Ford, N. J., Freed, A. D., & Luchko, Y. (2005) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2004.06.006 · Cited by 684
Initial value problems in discrete fractional calculus
Atici, F. M., & Eloe, P. W. (2008) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-08-09626-3 · Cited by 675
Hamiltonian Chaos and Fractional Dynamics
Zaslavskiî, G. M. (2005) · Medical Entomology and Zoology · Cited by 570
Cited by
Chaos in fractional-order discrete neural networks with application to image encryption
Chen, L., Yin, H., Huang, T., Yuan, L., Zheng, S., & Yin, L. (2020) · Neural Networks · doi:10.1016/j.neunet.2020.02.008 · Cited by 255
Metadata
- Authors
- Abdeljawad, T.
- Venue
- Computers & Mathematics with Applications
- Publisher
- Elsevier BV
- Published
- 2011-08
- Volume
- 62
- Issue
- 3
- Pages
- 1602-1611
- ISSN
- 0898-1221 (ISSN-L)
- OpenAlex
- W2088303893
- Cited by
- 733
- References
- 7
- FWCI
- 17.84
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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