Generalized fractional of the extended Nikiforov–Uvarov method for heavy tetraquark masses spectra

Abu‐Shady, M.; Ahmed, M. M. A.; Gerish, N. H.

doi:10.1142/s0217732323500281

Cited by 3 publications

(5 citation statements)

References 37 publications

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“…In Table II, with fractional parameters α = 0.79 and β = 0.65, we can calculate charmonium spectrum mass in different states; these results are better than those reported in recent Refs [39,41,42]. The calculated values for ground states 1S and 1P were close to experimental data which indicates that our calculation was accurate.…”

Section: Diquarksupporting

confidence: 68%

“…Additionally, we point out that there is a good agreement between our findings and those of the current Refs. [39,[41][42][43][44]. According to Table III, we found a total error for bottomonium mass of 0.65% in our study, which is lower than the total error found in those works.…”

Section: Diquarkcontrasting

confidence: 65%

“…We also noticed that the addition of the spin-spin interaction and the harmonic force to the potential found in research [41] led to improvement in the result and a reduction in the total error rate from 2.38% to 1.95% in charmomium masses, and bottomonium mass from 0.69% to 0.65%. Both pentaquark and heavy diquark systems were used to assess the method.…”

Section: Discussionmentioning

confidence: 71%

“…[ Schrödinger equation with Cornell potential and harmonic potential has been solved with the generalized fractional derivative in Ref. [41]. In Ref.…”

Section: Diquarkmentioning

confidence: 99%

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The spectra masses for heavy pentaquark using generalized fractional of the extended Nikiforov-Uvaro method

Abu-Shady,

Gerish

2024

Rev. Mex. Fís.

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The Nikiforov-Uvarov method is an efficient technique for solving of heavy diquark systems. It has been used to derive analytic-exact energy eigenvalues and eigenfunctions in fractional forms, which are useful in describing such systems. The potentials employed include the Cornell potential, harmonic potential, and spin-spin interaction; have been updated with respect to previous studies. Mass spectra of heavy pentaquarks were also calculated using this method. Compared to previous studies, the present results exhibit good experimental data agreement and are improved. We deduce that the fractional models contribute greatly to the heavy pentaquark masses.

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Section: Diquarksupporting

confidence: 68%

Section: Diquarkcontrasting

confidence: 65%

Section: Discussionmentioning

confidence: 71%

“…[ Schrödinger equation with Cornell potential and harmonic potential has been solved with the generalized fractional derivative in Ref. [41]. In Ref.…”

Section: Diquarkmentioning

confidence: 99%

See 2 more Smart Citations

The spectra masses for heavy pentaquark using generalized fractional of the extended Nikiforov-Uvaro method

Abu-Shady,

Gerish

2024

Rev. Mex. Fís.

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“…The generalized fractional derivative (GFD) is a novel concept for the fractional derivative that produces results consistent with those of classical definitions, was recently proposed by Abu-Shady and Kaabar 42 . The extended NU method was employed in conjunction with the GFD to solve the SE and determine the masses of heavy mesons 43 and also the mass spectra of heavy tetraquarks and diquark 44 . The masses of heavy flavor baryons with and without hyperfine interactions were calculated using the generalized fractional iteration approach in Ref.…”

Section: Introductionmentioning

confidence: 99%

A precise estimation for vibrational energies of diatomic molecules using the improved Rosen–Morse potential

Abu‐Shady

Khokha²

2023

Sci Rep

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In the context of the generalized fractional derivative, novel solutions to the D-dimensional Schrödinger equation are investigated via the improved Rosen-Morse potential (IRMP). By applying the Pekeris-type approximation to the centrifugal term, the generalized fractional Nikiforov-Uvarov method has been used to derive the analytical formulations of the energy eigenvalues and wave functions in terms of the fractional parameters in D-dimensions. The resulting solutions are employed for a variety of diatomic molecules (DMs), which have numerous uses in many fields of physics. With the use of molecular parameters, the IRMP is utilized to reproduce potential energy curves for numerous DMs. The pure vibrational energy spectra for several DMs are determined using both the fractional and the ordinary forms to demonstrate the effectiveness of the method utilized in this work. As compared to earlier investigations, it has been found that our estimated vibrational energies correspond with the observed Rydberg-Klein-Rees (RKR) data much more closely. Moreover, it is observed that the vibrational energy spectra of different DMs computed in the existence of fractional parameters are superior to those computed in the ordinary case for fitting the observed RKR data. Thus, it may be inferred that fractional order significantly affects the vibrational energy levels of DMs. Both the mean absolute percentage deviation (MAPD) and average absolute deviation (AAD) are evaluated as the goodness of fit indicators. According to the estimated AAD and MAPD outcomes, the IRMP is an appropriate model for simulating the RKR data for all of the DMs under investigation.

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Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative

Martínez,

Kaabar,

Martínez

2024

MCA

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In this article, new results are investigated in the context of the recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation. As in the classical case, the generalized Legendre polynomials constitute notable solutions to the aforementioned fractional differential equation. In the sense of the fractional derivative of Abu-Shady–Kaabar, we establish important properties of the generalized Legendre polynomials such as Rodrigues formula and recurrence relations. Special attention is also devoted to another very important property of Legendre polynomials and their orthogonal character. Finally, the representation of a function f∈Lα2([−1,1]) in a series of generalized Legendre polynomials is addressed.

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Generalized fractional of the extended Nikiforov–Uvarov method for heavy tetraquark masses spectra

Cited by 3 publications

References 37 publications

The spectra masses for heavy pentaquark using generalized fractional of the extended Nikiforov-Uvaro method

The spectra masses for heavy pentaquark using generalized fractional of the extended Nikiforov-Uvaro method

A precise estimation for vibrational energies of diatomic molecules using the improved Rosen–Morse potential

Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative

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