On conformable fractional calculus
Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calcul...
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| Published in | Journal of computational and applied mathematics Vol. 279; pp. 57 - 66 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.05.2015
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall’s inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed. |
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| AbstractList | Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall’s inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed. |
| Author | Abdeljawad, Thabet |
| Author_xml | – sequence: 1 givenname: Thabet surname: Abdeljawad fullname: Abdeljawad, Thabet email: tabdeljawad@psu.edu.sa organization: Department of Mathematics and General Sciences, Prince Sultan University-Riyadh-KSA, Saudi Arabia |
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| Cites_doi | 10.1155/2012/406757 10.1090/S0025-5718-1988-0929549-2 10.1090/S0002-9939-08-09626-3 10.1186/1687-1847-2013-36 10.1016/j.cam.2014.01.002 |
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| References | Samko, Kilbas, Marichev (br000005) 1993 K.S. Miller, B. Ross, Fractional difference calculus, in: Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications, Nihon University, Koriyama, Japan, (1989), 139–152. Podlubny (br000010) 1999 Abdeljawad (br000040) 2013; 2013 Abdeljawad, Atıcı (br000035) 2012; 2012 Kilbas, Srivastava, Trujillo (br000015) 2006; vol. 204 Khalil, Al Horani, Yousef, Sababheh (br000045) 2014; 264 Atıcı, Eloe (br000030) 2009; 137 Gray, Zhang (br000020) 1988; 50 Podlubny (10.1016/j.cam.2014.10.016_br000010) 1999 Kilbas (10.1016/j.cam.2014.10.016_br000015) 2006; vol. 204 Khalil (10.1016/j.cam.2014.10.016_br000045) 2014; 264 10.1016/j.cam.2014.10.016_br000025 Atıcı (10.1016/j.cam.2014.10.016_br000030) 2009; 137 Samko (10.1016/j.cam.2014.10.016_br000005) 1993 Abdeljawad (10.1016/j.cam.2014.10.016_br000035) 2012; 2012 Gray (10.1016/j.cam.2014.10.016_br000020) 1988; 50 Abdeljawad (10.1016/j.cam.2014.10.016_br000040) 2013; 2013 |
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