The effect of deformation of special relativity by conformable derivative

Al-Jamel, Ahmed; Al-Masaeed, Mohamed.; Rabei, Eqab M.; Băleanu, Dumitru

doi:10.31349/revmexfis.68.050705

Cited by 2 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition the conformable harmonic oscillator is quantized by using α -creation and α -annihilation operators [32]. Furthermore, the deformation of special relativity is articulated in the context of conformable derivatives [33]. Recently, more than one equation has been solved and the behavior of the solution is studied using conformable calculus such as (Laguerre differential equation [34], Angular equation of the Schrodinger Equation [35] and Schrodinger equation with Hydrogen atom [36] )…”

Section: Introductionmentioning

confidence: 99%

Quantization of the Bateman damping system with conformable derivative

AlBanwa¹,

Al-Jamel²,

Rabei³

et al. 2023

Preprint

View full text Add to dashboard Cite

In this work, the conformable Bateman Lagrangian for the damped harmonic oscillator system is proposed using the conformable derivative concept. In other words, the integer derivatives are replaced by conformable derivatives of order α with 0 < α ≤ 1. The corresponding conformable Euler-Lagrange equations of motion and fractional Hamiltonian are then obtained. The system is then canonically quantized and the conformable Schrodinger equation is constructed. The fractional-order dependence of the energy eigenvalues E α n and eigenfunctions ψ α n are obtained using using suitable transformations and the extended fractional Nikiforov-Uvarov method. The corresponding conformable continuity equation is also derived and the probability density and probability current are thus suitably defined. The probability density evolution as well as its dependence on α is plotted and analyzed for various situations. It is found that the energy eigenvalues are real and there are sort of gradual ordering in the behavior of the probability densities.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantization of the Bateman damping system with conformable derivative

AlBanwa¹,

Al-Jamel²,

Rabei³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

On the Geometric and Physical Properties of Conformable Derivative

Has,

Yılmaz,

Baleanu

2024

Mathematical Sciences and Applications E-Notes

Self Cite

View full text Add to dashboard Cite

In this article, we explore the advantages and geometric and physically implications of the conformable derivative. One of the key benefits of the conformable derivative is its ability to approximate the tangent at points where the classical tangent is not readily available. By employing conformable derivatives, alternative tangents can be created to overcome this limitation. Thanks to these alternative (conformable) tangents, physical interpretation can be made with alternative velocity vectors. Furthermore, the conformable derivative proves to be valuable in situations where the tangent plane cannot be defined. It enables the creation of alternative tangent planes, offering a solution in cases where the traditional approach falls short. Geometrically speaking, the conformable derivative carries significant meaning. It provides insights into the local behavior of a function and its relationship with nearby points. By understanding the conformable derivative, we gain a deeper understanding of how a function evolves and changes within its domain. To enhance comprehension and visualize the concepts discussed, the article presents several examples. These examples are accompanied by visual representations generated using the Mathematica program, aiding in a clearer understanding of the proposed ideas. By combining theoretical explanations, practical examples, and visualizations, this article aims to provide a comprehensive exploration of the advantages and geometric and physically implications of the conformable derivative.

show abstract

The effect of deformation of special relativity by conformable derivative

Cited by 2 publications

References 26 publications

Quantization of the Bateman damping system with conformable derivative

Quantization of the Bateman damping system with conformable derivative

On the Geometric and Physical Properties of Conformable Derivative

Contact Info

Product

Resources

About