• Analytical study of $D$-dimensional fractional Klein–Gordon equation with a fractional vector plus a scalar potential

• Fulltext

https://www.ias.ac.in/article/fulltext/pram/094/0033

• Keywords

Fractional Klein–Gordon equation; power series method; fractional Coulomb potential; Mittag– Leffler function

• Abstract

$D$-dimensional fractional Klein–Gordon equation with fractional vector and scalar potential has been studied. Both fractional potentials are taken as attractive Coulomb-type with different multiplicative parameters, namely $v$ and $s$. Jumarie-type definitions for fractional calculus have been used. We have succeeded in achieving Whittaker-type classical differential equation in fractional mode for the required eigenfunction. Fractional Whittaker equation has been manipulated using the behaviour of the eigenfunction at asymptotic distance and origin. This manipulation delivers fractional-type confluent hypergeometric equation to solve. Power series method has been employed to do the task. All the obtained results agree with the existing results in literature when fractional parameter $\alpha$ is unity. Finally, we furnish numerical results with a few eigenfunction graphs for different spatial dimensions and fractional parameters.

• Author Affiliations

1. Kodalia Prasanna Banga High School (H.S), South 24 Parganas, Kolkata 700 146, India
2. Department of Applied Mathematics, University of Calcutta, Kolkata 700 009, India
3. Reactor Control System Design Section (E & I Group), Bhabha Atomic Research Centre, Mumbai 400 085, India

• Pramana – Journal of Physics

Volume 96, 2022
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Posted on July 25, 2019