Chin. Phys. Lett.  2017, Vol. 34 Issue (2): 020201    DOI: 10.1088/0256-307X/34/2/020201
GENERAL |
A New Fractional Model for the Falling Body Problem
A. Ebaid1**, B. Masaedeh1, E. El-Zahar2,3
1Department of Mathematics, Faculty of Science, Tabuk University, P. O. Box 741, Tabuk 71491, Kingdom of Saudi Arabia
2Department of Mathematics, Faculty of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj, 11942, Kingdom of Saudi Arabia
3Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom, 32511, Menofia University, Egypt
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Abstract Recently, a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantages over the preceding definitions. For mathematical models in applied sciences and to preserve the dimensionality of the physical quantities, an auxiliary parameter ($\sigma$) which has the dimension of seconds should be implemented in the fractional derivative definition. We obtain analytic solutions for the resulting conformable fractional differential equations describing the vertical velocity and the height of the falling body. It is shown that the dimensions of velocity and height are always correct without any restrictions on the auxiliary parameter $\sigma$ which contradicts with the results in the literature when applying the Caputo definition to the same problem. This may open the door for many future works either to describe the role of such an auxiliary parameter or to derive a more suitable definition for the fractional derivative.
Received: 05 October 2016      Published: 25 January 2017
PACS:  02.30.Hq (Ordinary differential equations)  
  46.15.-x (Computational methods in continuum mechanics)  
  47.10.A- (Mathematical formulations)  
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A. Ebaid, B. Masaedeh, E. El-Zahar 2017 Chin. Phys. Lett. 34 020201
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http://cpl.iphy.ac.cn/10.1088/0256-307X/34/2/020201       OR      http://cpl.iphy.ac.cn/Y2017/V34/I2/020201
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A. Ebaid
B. Masaedeh
E. El-Zahar
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