The Influence of Fractional Derivatives on Thermodynamic Properties by Studying the CPSEHP Interaction
Abstract
The parametric Nikiforov-Uvarov (N-U) method is employed in conjunction with a generalized fractional derivative (GFD) to investigate the energy eigenvalues and the total normalized wave function associated with the Coulomb plus screened exponential hyperbolic potential (CPSEHP) in terms of Jacobi polynomials. This potential exhibit maximum effectiveness at lower values of the screening parameter. To explore the thermal and superstatistical characteristics, the derived energy eigenvalues are directly incorporated into the partition function (Z) and subsequently used to determine other thermodynamic quantities, including vibrational mean energy (U), specific heat capacity (C), entropy (S), and free energy (F). Comparisons with previous studies are conducted. The classical case is recovered from the fractional case by setting α = β = 1, consistent with prior work. Our results demonstrate that the fractional parameter plays a crucial role in governing the thermal and superstatistical properties within the framework of this model.
Downloads
References
M. Dalir, and M. Bashour, Appl. Math. Sci. 4, 1021 (2010).
M. Abu-Shady, Int. J. Mod. Phys. A, 34(31), 1950201 (2019). https://doi.org/10.1142/S0217751X19502014
N. Jamshir, B. Lari, and H. Hassanabadi, Stat. Mech. Appl. Phys. A, 565, 125616 (2021). https://doi.org/10.1016/j.physa.2020.125616
M. Abu-Shady, and Sh.Y. Ezz-Alarab, Few-Body. Syst. 62, 13 (2021). https://doi.org/10.1007/s00601-021-01591-7
M. Abu-Shady, A.I. Ahmadov, H.M. Fath-Allah, and V.H. Badalov, J. Theor. Appl. Phys. 16, 3 (2022). https://doi.org/10.30495/jtap.162225
A. Al-Jamel, Int. J. Mod. Phys. A, 34, 1950054 (2019). https://doi.org/10.1142/S0217751X19500544
M.M. Hammad, A.S. Yaqut, M.A. Abdel-Khalek, and S.B. Doma, Nuc. Phys. A, 1015, 122307 (2021). https://doi.org/10.1016/j.nuclphysa.2021.122307
G. Wang, and A.M. Wazwaz, Chaos. Solit. Fract. 155, 111694 (2022). https://doi.org/10.1016/J.CHAOS.2021.111694
M. Abu-Shady, and M.K.A. Kaabar, Math. Prob. Eng. 2021, 9444803 (2021). https://doi.org/10.1155/2021/9444803
M. Abu-Shady, and E. M. Khokha, Advances in High Energy Physics. 2018, 7032041 (2018). https://doi.org/10.1155/2018/7032041
M. Abu-Shady, and H. M. Fath-Allah, Int. J. Mod. Phys. A, 35, 2050110 (2020). https://doi.org/10.1142/S0217751X20501109
M. Abu-Shady, and A. N. Ikot, Eur, Phys. J. Plus. 135, 321 (2019). https://doi.org/10.1140/epjp/i2019-12685-y
M. Abu-Shady, E. M. Khokha, T. A. Abdel-Karim, European Physical Journal D, 76(9), 159 (2022). https://doi.org/10.1140/epjd/s10053-022-00480-w
H. Karayer, D. Demirhan, and F. Büyükkılıç, Comm. Theor. Phys. 66, 12 (2016). https://doi.org/10.1088/0253-6102/66/1/012
C. Tezcan, and R. Sever, Int. J. Theor. Phys. 48, 337 (2009). https://doi.org/10.1007/s10773-008-9806-y
A. Berkdemir, C. Berkdemir, and R. Sever, Modern Phys. Lett. A, 21, 2087 (2006). https://doi.org/10.1142/S0217732306019906
M. C. Zhang, G.H. Sun, SH. Dong, Phys. Lett A, 374, 704 (2010). https://doi.org/10.1016/j.physleta.2009.11.072
G. Chen, Zeitschrift für Naturforschung A, 59, 875 (2004). https://doi.org/10.1515/zna-2004-1124
S. M. Al-Jaber, Int. J. Theor. Phys. 47, 1853 (2008). https://doi.org/10.1007/s10773-007-9630-9
K. J. Oyewumi, F. O. Akinpelu, and A.D. Agboo, Int. J. Theor. Phys. A, 47, 1039 (2008). https://doi.org/10.1007/s10773-007-9532-x
S. Ikhdair, and R. Sever, J. Mole. Struc. 855, 13 (2008). https://doi.org/10.1016/j.theochem.2007.12.044
H. Hassanabadi, S. Zarrinkamar, and A.A. Rajabi, Comm. Theor. Phys. 55, 541 (2011). https://doi.org/10.1088/0253-6102/55/4/01
S. Ikhdair, and R. Sever, Int. J. Modern Phys. C, 19, 221 (2008). https://doi.org/10.1142/S0129183108012030
R. Kumar, and F. Chand, Commun. Theor. Phys. 59, 528 (2013). https://doi.org/10.1088/0253-6102/59/5/02
S.M. Kuchin, and N.V. Maksimenko, Univ. J. Phys. Appl. 7, 295 (2013). https://doi.org/10.13189/ujpa.2013.010310
M. Abu-Shady, H. Mansour, and A.I. Ahmadov, Advances in High Energy Physics, 2019, 4785615 (2019). https://doi.org/10.1155/2019/4785615
M. Abu-Shady and E. M. Khokha, International Journal of Modern Physics A, 36(29), 2150195 (2021). https://doi.org/10.1142/S0217751X21501955
M. Abu-Shady, T. A. Abdel-Karim, and E. M. Khokha, Advances in High Energy Physics, 2018, 356843 (2018). https://doi.org/10.1155/2018/7356843
A.N. Ikot, O.A. Awoga, and A.D. Antia, Chinese Phys. B, 22, 2 (2013). https://doi.org/10.1088/1674-1056/22/2/020304
D. Agboola, Phys. Scripta. 80, 065304 (2009). https://doi.org/10.1088/0031-8949/80/06/065304
H. Hassanabadi, B.H. Yazarloo, S. Zarrinkamar, and M. Solaimani, Int. J. Quant. Chem. 112, 3706 (2012). https://doi.org/10.1002/qua.24064
H. Hassanabadi, E. Maghsoodi, A. N. Ikot, and S. Zarrinkamar, Appl. Math. Comput. 219, 9388 (2013). https://doi.org/10.1016/j.amc.2013.03.011
Wahyulianti, A. Suparmi, C. Cari, and F. Anwar, J. Phys. Conf. Serie. 795, 012022 (2017). https://doi.org/10.1088/1742-6596/795/1/012022
S. Flugge, Practical Quantum Mechanics, (Springer-Verlag, 1974).
C. A. Onate, I. B. Okon, U.E. Vincent, E.S. Eyube, M.C. Onyeaju, E. Omugbe, and G.O. Egharevba, Sci. Rep. 12, 15188 (2022). https://doi.org/10.1038/s41598-022-19179-4
C.O. Edet, U.S. Okorie, G. Osobonge, A.N. Ikot, G.J. Rampho, and R. Sever, J. Math. Chem. 58, 989 (2020). https://doi.org/10.1007/s10910-020-01107-4
A.N. Ikot, E.O. Chukwuocha, M.C. Onyeaju, C.A. Onnle, B.I. Ita, and M.E. Udoh, Pramana – J. Phys. 90, 22 (2018). https://doi.org/10.1007/s12043-017-1510-0
C.A. Onate, Chinese J. Phys. 54, 165 (2016). https://doi.org/10.1016/j.cjph.2016.04.001
I.B. Okon, O.O. Popoola, E. Omugbe, A.D. Antia, C.N. Isonguyo, and E.E. Ituen, Comput. Theor. Chem. 1196, 11132 (2021). https://doi.org/10.1016/j.comptc.2020.113132
K.J. Oyewumi, B.J. Falaye, C.A. Onate, O.J. Oluwadare, and W.A. Yahya, Molec. Phys. 112, 127 (2014). https://doi.org/10.1080/00268976.2013.804960
A. Boumali, and H. Hassanabadi, Eur. Phys. J. Plus. 128, 124 (2013). https://doi.org/10.1140/epjp/i2013-13124-y
M. Abu-Shady, and H.M. Fath-Allah, East. Eur. J. Phys. (3), 248 (2023). https://doi.org/10.26565/2312-4334-2023-3-22
M. Rashdan, M. Abu-Shady, and T.S.T. Ali, Int. J. Mod. Phys. E, 15(1), 143 (2006). https://doi.org/10.1142/S0218301306003965
M. Abu-Shady, Int. J. Mod. Phys. E, 21, 1250061 (2012). https://doi.org/10.1142/S0218301312500619
M.M. Hammad, et al., Nucl. Phys. A, 1015, 122307 (2021). https://doi.org/10.1016/j.nuclphysa.2021.122307
A.F. Nikiforov, and V.B. Uvarov, Special Functions of Mathematical Physics, (Birkhuser, Basel), (1988).
I. Okon, C. Onate, E. Omugbe, U. Okorie, et. al., Advances in High Energy Physics, 2022, 5178247 (2022). https://doi.org/10.1155/2022/5178247
C. Beck, “Superstatistics: theory and applications,” Continuum. Mech. Thermodyn. 16, 293 (2004). https://doi.org/10.1007/s00161-003-0145-1
C. Beck, and E.G. Cohen, arXiv:cond-mat/0205097v2 14 Nov 2002.
C.O. Edet, P.O. Amadi, U.S. Okorie, A. Tas, A.N. Ikot, and G. Rampho, Revista Mexicana de Fısica. 66, 824 (2020). https://doi.org/10.31349/RevMexFis.66.824
I. Okon, C. Onate, E. Omugbe, et. al., Advances in High Energy Physics, 2022, 178247, (2022). https://doi.org/10.1155/2022/5178247
E.P. Inyang, F. Ayedun, E.A. Ibanga, M.K. Lawal, et. al., Result. Phys. 43, 106075 (2022). https://doi.org/10.1016/j.rinp.2022.106075
B.I. Okon, O. Popoola, E. Omugbe, D.A. Antia, et. al., Comput. Theor. Chem. 1196, 113112 (2021).
P.E. Inyang, P.E. Inyang, I.O. Akpan, J.E. Ntibi, and E.S. William, Canad. J. Phys. 99, 982 (2021). https://doi.org/10.1139/cjp-2020-0578
M. Abu-Shady, and Sh.Y. Ezz-Alarab, India. J. Phys. 97, 3661 (2023). https://doi.org/10.1007/s12648-023-02695-y
V. Kumar, S.B. Bhardwa, R.M. Singh, and F. Chand, Pramana. J. Phys. 96, 125 (2022). https://doi.org/10.1007/s12043-022-02377-0
H. Hassanabadi, M. Hosseinpoura, Eur. Phys. J. C, 76, 553 (2016). https://doi.org/10.1140/epjc/s10052-016-4392-2
H.G. Mansour, and A. Gamal, Advances in High Energy Physics, 7, 7269657 (2018). https://doi.org/10.1155/2018/7269657
P.E. Inyang, O.E. Obisung, S.E. William, and B.I. Okon, East. Eur. J. Phys. (3), 104 (2022). https://doi.org/10.26565/2312-4334-2022-3-14
K.J. Oyewum, B.J. Falaye, C.A. Onate, O.J. Oluwadare, and W.A. Yahya, Molec. Phys. 112, 127 (2014). https://doi.org/10.1080/00268976.2013.804960
D. Ebert, R. N. Faustov, V.O. Galkin, Phys. Rev. D, 67, 014027, (2003). https://doi.org/10.1103/PhysRevD.67.014027
M. Abu-shady, and H.M. Fath-Allah, Advances in High Energy Physics, 2022, 4539308 (2022). https://doi.org/10.1155/2022/4539308
H. Hassanabadi, and M. Hosseinpour, Eur. Phys. J. C, 76, 553 (2016). https://doi.org/10.1140/epjc/s10052-016-4392-2
A.N. Ikot, U.S. Okorie, G. Osobonye, P.O. Amadi, C.O. Edet, et al., Heliyon. 6, e03738 (2020). https://doi.org/10.1016/j.heliyon.2020.e03738
H. Hassanabadi, M. Hosseinpoura, Eur. Phys. J. C, 76, 553 (2016). https://doi.org/10.1140/epjc/s10052-016-4392-2
Copyright (c) 2025 M. Abu-Shady, Sh. Y. Ezz-Alarab
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
