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Entropy 2016, 18(2), 1; doi:10.3390/e18020001

New Derivatives on the Fractal Subset of Real-Line

1
Department of Physics, College of Science, Urmia Branch, Islamic Azad University, Urmia, Iran
2
Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey
3
Institute of Space Sciences, P.O. BOX, MG-23, R 76900 Magurele-Bucharest, Romania
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editors: J. Tenreiro Machado and António M. Lopes
Received: 6 October 2015 / Revised: 4 December 2015 / Accepted: 15 December 2015 / Published: 29 January 2016
(This article belongs to the Special Issue Complex and Fractional Dynamics)
View Full-Text   |   Download PDF [258 KB, uploaded 29 January 2016]   |  

Abstract

In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect. View Full-Text
Keywords: fractal calculus; triadic Cantor set; non-local Laplace transformation; memory processes; generalized Mittag-Leffler function; generalized gamma function; generalized beta function fractal calculus; triadic Cantor set; non-local Laplace transformation; memory processes; generalized Mittag-Leffler function; generalized gamma function; generalized beta function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Khalili Golmankhaneh, A.; Baleanu, D. New Derivatives on the Fractal Subset of Real-Line. Entropy 2016, 18, 1.

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