Page 86 - IJOCTA-15-1

E.M. Rabei et al. / IJOCTA, Vol.15, No.1, pp.71-81 (2025)

[20] Weisskopf, V. F. (1939). On the self-energy and [33] Al-Masaeed, M., Rabei, E. M.,& Al-Jamel, A.
the electromagnetic field of the electron. Physical (2022). Extension of the variational method to
Review, 56(1), 72. https://doi.org/10.1103/ conformable quantum mechanics. Mathematical
PhysRev.56.72 Methods in the Applied Sciences, 45(5), 2910–
[21] Matos-Abiague, A.(2001). Deformation of quan- 2920. https://doi.org/10.1002/mma.7963
tum mechanics in fractional-dimensional space. [34] Al-Masaeed, M. G., Rabei, E. M., & Al-Jamel,
Journal of Physics A: Mathematical and General, A. (2024). Analytical Solution of Conformable
34(49), 11059. https://doi.org/10.1088/0305 Schr¨odinger Wave Equation with Coulomb Po-
-4470/34/49/321 tential. Progress in Fractional Differentiation and
[22] Oldham, K., & Spanier, J. (1974). Elsevier. Applications, 10, 137–147.
The fractional calculus theory and applications [35] Al-Masaeed, M., Rabei, E. M., Al-Jamel, A.,
of differentiation and integration to arbitrary or- & Baleanu, D. (2021). Extension of perturba-
der.London. tion theory to quantum systems with conformable
[23] Prajapati, J. C., Patel, A. D., Pathak, K. N., derivative. Modern Physics Letters A, 36(32),
& Shukla, A. K. (2012). Fractional calculus ap- 2150228. https://doi.org/10.1142/S02177
proach in the study of instability phenomenon in 3232150228X
fluid dynamics. Palestine Journal of Mathemat- [36] Al-Masaeed, M., Rabei, E. M., & Al-Jamel, A.
ics, 1(2), 95–103. (2022). Wkb approximation with conformable
[24] Caputo, M. (1967). Linear models of dissipation operator. Modern Physics Letters A, 37(22),
whose Q is almost frequency independent-II. Geo- 2250144. https://doi.org/10.1142/S02177
physical Journal International, 13(5), 529–539. 32322501449
https://doi.org/10.1111/j.1365-246X.19 [37] Hammad, M. M., Yaqut, A. S., Abdel-Khalek,
67.tb02303.x M. A., & Doma, S. B. (2021). Analytical
[25] Grunwald, A. K. (1867). Uber” begrente” Deriva- study of conformable fractional Bohr Hamilton-
tionen und deren Anwedung. Zangew Math und ian with Kratzer potential. Nuclear Physics A,
Phys, 12, 441–480. 1015, 122307. https://doi.org/10.1016/j.nu
[26] Riesz, M. (1939). L’int´egrale de Riemann- clphysa.2021.122307
Liouville et le probl´eme de Cauchy pour [38] Hammad, M. M. (2021). On the conformable
l’´equation des ondes. Bulletin de la Soci´et´e fractional E(5) critical point symmetry. Nuclear
Math´ematique de France, 67, 153–170. https: Physics A, 1011, 122203. https://doi.org/10
//doi.org/10.24033/bsmf.1309 .1016/j.nuclphysa.2021.122203
[27] Weyl, H. (1917). Bemerkungen zum begriff [39] Sher, M., Khan, A., Shah, K., & Abdeljawad,
des differentialquotienten gebrochener ordnung. T. (2023). Existence and stability theory of pan-
Vierteljschr. Naturforsch. Gesellsch. Zurich, tograph conformable fractional differential prob-
62(1-2),296–302. lem. Thermal Science, 27(Spec. issue 1), 237–244.
[28] Jarad, F., Abdeljawad, T., & Baleanu, D. https://doi.org/10.2298/TSCI23S1237S
(2012). On Riesz-Caputo Formulation for Sequen- [40] Koyunbakan, H., Shah, K., & Abdeljawad, T.
tial Fractional Variational Principles. Abstract (2023). Well-posedness of inverse Sturm–Liouville
and Applied Analysis, 2012(1),890396. https: problem with fractional derivative. Qualitative
//doi.org/10.1155/2012/890396 Theory of Dynamical Systems, 22(1), 23. https:
[29] Khalil, R., Al Horani, M., Yousef, A.,& Sabab- //doi.org/10.1007/s12346-022-00727-2
heh, M. (2014). A new definition of fractional de- [41] Sher, M., Khan, A., Shah, K., Sarwar, M.,
rivative. Journal of Computational and Applied Alqudah, M. A., & Abdeljawad, T. (2023). Math-
Mathematics, 264, 65–70. https://doi.org/10 ematical analysis of fractional order alcoholism
.1016/j.cam.2014.01.002 model. Alexandria Engineering Journal, 78, 281–
[30] Abdeljawad, T. (2015). On conformable fractional 291. https://doi.org/10.1016/j.aej.2023.0
calculus. Journal of computational and Applied 7.010
Mathematics, 279, 57–66. https://doi.org/10 [42] Eiman., Shah, K., Hleili, M., & Abdeljawad, T.
.1016/j.cam.2014.10.016 (2024). Two strains model of infectious diseases
[31] Atangana, A., Baleanu, D., & Alsaedi, A. (2015). for mathematical analysis and simulations. Math-
New properties of conformable derivative. Open ematical and Computer Modelling of Dynamical
Mathematics, 13(1), 000010151520150081. http Systems, 30(1), 477–495. https://doi.org/10
s://doi.org/10.1515/math-2015-0081 .1080/13873954.2024.2355940
[32] Chung, W. S., Zare, S., Hassanabadi, H., & [43] Khan, S. (2024). Existence theory and stability
Maghsoodi, E. (2020). The effect of fractional cal- analysis to a class of hybrid differential equa-
culus on the formation of quantum-mechanical tions using confirmable fractal fractional deriva-
operators. Mathematical Methods in the Applied tive. Journal of Fractional Calculus and Nonlin-
Sciences, 43(11), 6950–6967. https://doi.org/ ear Systems, 5(1), 1-11. https://doi.org/10.4
10.1002/mma.6445 8185/jfcns.v5i1.1103

80