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Novel Fractional Models Compatible with Real World Problems

by Ramazan Ozarslan *,†, Ahu Ercan and Erdal Bas
Department of Mathematics, Faculty of Science, Firat University, Elazig 23119, Turkey
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Fractal Fract 2019, 3(2), 15; https://doi.org/10.3390/fractalfract3020015
Received: 9 March 2019 / Revised: 26 March 2019 / Accepted: 26 March 2019 / Published: 1 April 2019
In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville–Caputo fractional conformable derivative and the modified form of this new definition. We utilize the σ auxiliary parameter for preserving the dimension of physical quantities for newly defined fractional conformable vertical motion of a falling body problem in a resistant medium. The analytical solutions are obtained by iterating this new fractional integral and results are illustrated under different orders by comparison with the Liouville–Caputo fractional operator. View Full-Text
Keywords: fractional derivative; vertical motion of falling body problem; Malthusian growth equation fractional derivative; vertical motion of falling body problem; Malthusian growth equation
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Ozarslan, R.; Ercan, A.; Bas, E. Novel Fractional Models Compatible with Real World Problems. Fractal Fract 2019, 3, 15.

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