The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
What is a fractional derivative?
Abstract
This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grunwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.
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Citations
Cites
Theory and Applications of Fractional Differential Equations
Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006) · North-Holland mathematics studies · doi:10.1016/s0304-0208(06)x8001-5 · Cited by 14,200
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
A new definition of fractional derivative
Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2014.01.002 · Cited by 3,480
An Extension Problem Related to the Fractional Laplacian
Caffarelli, L., & Silvestre, L. (2007) · Communications in Partial Differential Equations · doi:10.1080/03605300600987306 · Cited by 2,337
Applied and Computational Complex Analysis
Thacher, H. C., & Henrici, P. (1977) · Mathematics of Computation · doi:10.2307/2005805 · Cited by 2,022
Recent history of fractional calculus
Machado, J. A. T., Kiryakova, V. S., & Mainardi, F. (2010) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2010.05.027 · Cited by 1,631
L'intégrale de Riemann-Liouville et le problème de Cauchy
Riesz, M. (1949) · Acta Mathematica · doi:10.1007/bf02395016 · Cited by 848
Fractional Calculus for Scientists and Engineers
Ortigueira, M. D. (2011) · Lecture Notes in Electrical Engineering · doi:10.1007/978-94-007-0747-4 · Cited by 780
Self-citationFractional differentiability of nowhere differentiable functions and dimensions
Kolwankar, K. M., & Gangal, A. D. (1996) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166197 · Cited by 361
Chen, W., & Holm, S. (2004) · The Journal of the Acoustical Society of America · doi:10.1121/1.1646399 · Cited by 348
Cited by
Atangana, A., & Gómez-Aguilar, J. F. (2018) · The European Physical Journal Plus · doi:10.1140/epjp/i2018-12021-3 · Cited by 425
A new buffering theory of social support and psychological stress
Bekiros, S., Jahanshahi, H., & Munoz-Pacheco, J. M. (2022) · PLOS ONE · doi:10.1371/journal.pone.0275364 · Cited by 54
Metadata
- Authors
- Ortigueira, M. D., & Tenreiro Machado, J. A.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2015-07
- Volume
- 293
- Pages
- 4-13
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W2036266090
- Cited by
- 511
- References
- 12
- FWCI
- 20.22
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ortigueira, M. D., & Tenreiro Machado, J. A. (2015). What is a fractional derivative? Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2014.07.019
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
