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Can Fractional Calculus be Applied to Relativity?

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Abstract

Interest has been recently devoted to historical and philosophical aspects about fractional calculus (FC) and its adoption as additional mathematical tool in different physics areas as well as in other scientific applications. However, potential application of FC towards relativity is still lacking. In relativity theory, Lorentz transformation of time and position coordinates plays a major role while the corresponding outcomes still defy our ‘common sense’ (e.g. time dilation and space contraction). As some problems in physics can be solved by following different mathematical routes leading to the same result, the present paper suggests an alternative method to relativity. Instead of converting time and position data from different inertial reference frames through Lorentz transformation, it is here envisaged to numerically adjust relativistic results with the help of FC. Bearing in mind well established postulates from relativity, we intend to fill up this gap by addressing and discussing the main arguments in favour of the prospective use of FC as emergent and alternative tool applied to relativity.

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Authors and Affiliations

  1. Systems Dynamics Group, University of São Paulo, Pirassununga Campus, Av. Duque de Caxias Norte 225, Pirassununga, SP, 13635-900, Brazil

    S. A. David & J. A. Rabi

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  1. S. A. David
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  2. J. A. Rabi
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Correspondence to S. A. David.

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David, S.A., Rabi, J.A. Can Fractional Calculus be Applied to Relativity?. Axiomathes 30, 165–176 (2020). https://doi.org/10.1007/s10516-019-09448-9

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