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A falling body problem through the air in view of the fractional derivative approach

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  • Fa, Kwok Sau

Abstract

Recent studies have revealed that the fractional derivative can behave as a dissipative term. The analysis of a simple fractional oscillator has supported this point of view. However, other physical aspects related to fractional derivative are also important to be explored. For this purpose, in this work, we employ the fractional approach and guide ourselves by the above property to investigate the falling body problem. We show that the velocity of a falling body, in the fractional approach, can be greater (t<1) or less (t>1) than that velocity of free-fall obtained by the usual approach. Moreover, we show that the fractional derivative alone is not sufficient to attain a terminal speed. In order to provide a terminal speed into the fractional system a term, proportional to velocity, must be introduced.

Suggested Citation

  • Fa, Kwok Sau, 2005. "A falling body problem through the air in view of the fractional derivative approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 199-206.
    • Handle: RePEc:eee:phsmap:v:350:y:2005:i:2:p:199-206
    DOI: 10.1016/j.physa.2004.11.041
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    Cited by:

    1. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    2. Turkyilmazoglu, Mustafa & Altanji, Mohamed, 2023. "Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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