Analytical solution for the dynamics and optimization of fractional Klein–Gordon equation: an application to quantum particle

Kashif Ali Abro, Ambreen Siyal, Abdon Atangana, Qasem M. Al-Mdallal

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Klein–Gordon equation characterizes spin-particles through neutral charge field within quantum particle. In this context, fractionalized Klein–Gordon equation is investigated for the comparative analysis of the newly presented fractional differential techniques with non-singularity among kernels. The non-singular and non-local kernels of fractional differentiations have been employed on Klein–Gordon equation for the development of governing equation. The analytical solutions of Klein–Gordon equation have been traced out by fractional techniques by means of Laplace transforms and expressed in terms of series form and gamma function. The data analysis of fractionalized Klein–Gordon equation is observed for Pearson's correlation coefficient, probable error and regression analysis. For the sake of comparative analysis of fractional techniques, 2D sketch, 3D pie chart, contour surface with projection and 3D bar sketch have been depicted on the basis of embedded parameters. Our results suggest that varying frequency has reversal trends for quantum wave and de Broglie wave.

Original languageEnglish
Article number704
JournalOptical and Quantum Electronics
Volume55
Issue number8
DOIs
Publication statusPublished - Aug 2023

Keywords

  • And regression analysis
  • Fractional techniques
  • Fractionalized Klein–Gordon equation
  • Pearson's correlation coefficient
  • Probable error

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Electrical and Electronic Engineering

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