Next Article in Journal
Relative Entropy in Biological Systems
Next Article in Special Issue
Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator
Previous Article in Journal
Entropy-Weighted Instance Matching Between Different Sourcing Points of Interest
Previous Article in Special Issue
Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent
Open AccessArticle

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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: J. Tenreiro Machado and António M. Lopes
Entropy 2016, 18(2), 1; https://doi.org/10.3390/e18020001
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)
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
Show Figures

Figure 1

MDPI and ACS Style

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

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop