Click here to view fulltext PDF

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

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

$D$-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.

TAPAS DAS¹ UTTAM GHOSH² SUSMITA SARKAR² SHANTANU DAS³

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

Published

30 January 2020

Manuscript received

19 August 2019

Manuscript revised

23 October 2019

Accepted

19 November 2019

Early published

Unedited version published online

Final version published online

30 January 2020