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    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/090/06/0074

    • Keywords

       

      Jumarie fractional derivative; Mittag–Leffler function; fractional Schrödinger equation; fractional wave function

    • Abstract

       

      Klein–Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein–Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein–Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein–Gordon equation, we can overcome the problem. The fractional Klein–Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

    • Author Affiliations

       

      UTTAM GHOSH1 JOYDIP BANERJEE2 SUSMITA SARKAR1 SHANTANU DAS3

      1. Department of Applied Mathematics, University of Calcutta, A.P.C. Road, Kolkata 700 009, India
      2. Uttar Buincha Kajal Hari Primary School, Fulia, Nadia 741 402, India
      3. Reactor Control Systems Design Section E and I Group, Bhabha Atomic Research Centre,Mumbai 400 085, India

    • Dates

       
      Published
      8 June 2018
      Manuscript received
      18 January 2017
      Manuscript revised
      1 December 2017
      Accepted
      7 December 2017
      Early published
      Unedited version published online
      Final version published online
      3 May 2018

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