We obtained exact eigenvalue and eigenfunction solutions of the local fractional KG equation and investigated the evolution of relativistic effects in correspondence with the fractional order.
📌 3 Key Takeaways
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Objective & Hypothesis:The one-dimensional Klein-Gordon (KG) equation is investigated in the domain of conformable fractional calculus for one-dimensional scalar potential, namely generalized Hulthen potential.
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Key Findings & Data:The conformable fractional calculus is based on conformable fractional derivative, which is the most natural definition in noninteger order calculus.
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Conclusion & Impact:We obtained exact eigenvalue and eigenfunction solutions of the local fractional KG equation and investigated the evolution of relativistic effects in correspondence with the fractional order.
The one-dimensional Klein-Gordon (KG) equation is investigated in the domain of conformable fractional calculus for one-dimensional scalar potential, namely generalized Hulthen potential. The conformable fractional calculus is based on conformable fractional derivative, which is the most natural definition in noninteger order calculus. Fractional order differential equations can be solved analytically by means of this derivative operator. We obtained exact eigenvalue and eigenfunction solutions of the local fractional KG equation and investigated the evolution of relativistic effects in correspondence with the fractional order.
KARAYER, H. H., DEMİRHAN, A. D., BÜYÜKKILIÇ, F. (2017). Analytical solution of the local fractional Klein-Gordon equation for generalized Hulthen potential. Turkish Journal of Physics, Cilt: 41 - Sayı: 6, 551–559. https://ajindex.com/articles/723909