On a Caputo-type fractional derivative
By D. S. Oliveira, E. Capelas de Oliveira. Advances in Pure and Applied Mathematics, 2018
60 citations recorded by the source corpus.
Abstract In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary order. Our differential operator recovers as limiting cases the arbitrary order derivatives proposed by Caputo and by Caputo–Hadamard. Some properties are presented as well as the relation between this differential operator of arbitrary order and the Katugampola generalized fractional operator. As an application we prove the fundamental theorem of fractional calculus associated with our operator.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/1ae10d1f84d0269daf18ef88c41cda742e5eebdd
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In Applied Mathematics
- Fahd Jarad
- Thabet Abdeljawad
- Dumitru Băleanu
- Mehmet Yavuz
- Arran Fernandez
- Y. Chu
- Guo-cheng Wu
- Saima Rashid
In Modeling and Simulation
- Fahd Jarad
- Thabet Abdeljawad
- Dumitru Băleanu
- Arran Fernandez
- Mehmet Yavuz
- Chokkalingam Ravichandran
- Hafiz Muhammad Fahad
- Y. Chu
Citations in the corpus
- Generalized fractional derivatives and Laplace transform (2020, background): “Other types of new fractional derivatives can be found in [26, 27, 28, 23]”