Solution of conformable Laguerre and associated Laguerre equations using Laplace transform†

Rabei, Eqab M.; Al-Jamel, A.; Al-Masaeed, Mohamed.

doi:10.22541/au.165840662.24105558/v1

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…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

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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.

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Section: Introductionmentioning

confidence: 99%

Quantization of the Bateman damping system with conformable derivative

AlBanwa¹,

Al-Jamel²,

Rabei³

et al. 2023

Preprint

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“…[25] introduced Riemannian geometry through using the conformable fractional derivative in Christoffel index symbols of the first and second kind. The conformable calculus has been used in making an extension of approxima-tion methods to become applicable to conformable quantum mechanics [26][27][28], and to find solutions of related differential equations such as the conformable Laguerre and associated Laguerre equations [29]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

The effect of deformation of special relativity by conformable derivative

et al. 2022

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In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

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“…Another comparison, we notice that the constants of increases of the norms of the control bounded operators W and W −1 in the application of the work [27] are given directly in a simple way in terms of the exponential function, contrary, for the Caputo fractional derivative in the application of the nice work [51] these constants are given in terms of the so-called Mittag-Leffler function. For more details and conclusions concerning the uses and applications of conformable fractional calculus, we refer to the works [2,4,5,7,8,10,11,12,13,14,16,17,22,23,24,25,28,29,42,49].…”

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confidence: 99%