Global InformationKatugampola fractional operators information
In mathematics, Katugampola fractional operators are integral operators that generalize the Riemann–Liouville and the Hadamard fractional operators into a unique form.[1][2][3][4] The Katugampola fractional integral generalizes both the Riemann–Liouville fractional integral and the Hadamard fractional integral into a single form and It is also closely related to the Erdelyi–Kober[5][6][7][8] operator that generalizes the Riemann–Liouville fractional integral. Katugampola fractional derivative[2][3][4] has been defined using the Katugampola fractional integral[3] and as with any other fractional differential operator, it also extends the possibility of taking real number powers or complex number powers of the integral and differential operators.
- ^ Katugampola, Udita N. (2011). "New approach to a generalized fractional integral". Applied Mathematics and Computation. 218 (3): 860–865. arXiv:1010.0742. doi:10.1016/j.amc.2011.03.062. S2CID 27479409.
- ^ a b Katugampola, Udita N. (2011). On Generalized Fractional Integrals and Derivatives, Ph.D. Dissertation, Southern Illinois University, Carbondale, August, 2011.
- ^ a b c Cite error: The named reference
derivativewas invoked but never defined (see the help page). - ^ a b Cite error: The named reference
tranwas invoked but never defined (see the help page). - ^ Erdélyi, Arthur (1950–51). "On some functional transformations". Rendiconti del Seminario Matematico dell'Università e del Politecnico di Torino. 10: 217–234. MR 0047818.
- ^ Kober, Hermann (1940). "On fractional integrals and derivatives". The Quarterly Journal of Mathematics (Oxford Series). 11 (1): 193–211. Bibcode:1940QJMat..11..193K. doi:10.1093/qmath/os-11.1.193.
- ^ Fractional Integrals and Derivatives: Theory and Applications, by Samko, S.; Kilbas, A.A.; and Marichev, O. Hardcover: 1006 pages. Publisher: Taylor & Francis Books. ISBN 2-88124-864-0
- ^ Theory and Applications of Fractional Differential Equations, by Kilbas, A. A.; Srivastava, H. M.; and Trujillo, J. J. Amsterdam, Netherlands, Elsevier, February 2006. ISBN 0-444-51832-0