Rabei, Eqab M.; Al Horani, Mohammed Quantization of fractional singular Lagrangian systems using WKB approximation. (English) Zbl 1446.70040 Int. J. Mod. Phys. A 33, No. 36, Article ID 1850222, 9 p. (2018). Summary: In this paper, the fractional singular Lagrangian system is studied. The Hamilton-Jacobi treatment is developed to be applicable for fractional singular Lagrangian system. The equations of motion are obtained for the fractional singular systems and the Hamilton-Jacobi partial differential equations are obtained and solved to determine the action integral. Then the wave function for fractional singular system is obtained. Besides, to demonstrate this theory, the fractional Christ-Lee model is discussed and quantized using the WKB approximation. Cited in 2 Documents MSC: 70H20 Hamilton-Jacobi equations in mechanics 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:fractional derivatives; Hamilton-Jacobi; singular Lagrangian; Christ-Lee model; WKB approximation PDFBibTeX XMLCite \textit{E. M. Rabei} and \textit{M. Al Horani}, Int. J. Mod. Phys. A 33, No. 36, Article ID 1850222, 9 p. (2018; Zbl 1446.70040) Full Text: DOI References: [1] Dirac, P. A. M., Lectures on Quantum Mechanics, (Yeshiva University, New York, 1964). · Zbl 0141.44603 [2] Rabei, E. and Guler, Y., Phys. Rev. A46, 3513 (1992). [3] Rabei, E., Nawafleh, K. and Ghassib, H., Phys. Rev. A66, 02410 (2002). [4] Rabei, E., Turk. J. Phys.23, 1083 (1999). [5] Rabei, E., Int. J. Theor. Phys.42, 2097 (2003). [6] Agrawal, O. P., J. Appl. Mech.68, 339 (2001). [7] Rabei, E., Alhalholy, T. and Rousan, A., Int. J. Mod. Phys. A19, 3083 (2004). [8] Rabei, E., Alhalholy, T. and Taani, A., Turk. J. Phys.28, 213 (2004). [9] Rekhriashvili, S. Sh., Tech. Phys. Lett.30, 55 (2004). [10] Kilbas, A., Srivastava, H. and Trujillo, J., Theory and Applications of Fractional Differential Equations (Elsevier Science B.V., Amsterdam, 2006). · Zbl 1092.45003 [11] Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., J. Comput. Appl. Math.264, 65 (2014). [12] Abdeljawad, T., J. Comput. Appl. Math.279, 57 (2015). [13] Abu Hammad, M. and Khalil, R., Int. J. Differ. Equ. Appl.13, 177 (2014). [14] Abu Hammad, M. and Khalil, R., Int. J. Pure. Appl. Math.94, 215 (2014). [15] Abu Hammad, M. and Khalil, R., Amer. J. Comput. Appl. Math.4, 187 (2014). [16] Al Horani, M., Abu Hammad, M. and Khalil, R., J. Math. Comput. Sci.16, 147 (2016). [17] Khalil, R., Al Horani, M. and Anderson, D., J. Math. Comput. Sci.16, 140 (2016). [18] Rabei, E. and Ababneh, B., J. Math. Anal. Appl.344, 799 (2008). [19] Rabei, E., Al-Jamel, A., Widyan, H. and Baleanu, D., J. Math. Phys.55, 034101 (2014). · Zbl 1290.78003 [20] Rabei, E., Nawafleh, K., Hijjawi, R., Muslih, S. and Baleanu, D., J. Math. Anal. Appl.327, 891 (2007). [21] M. Lazo and D. Torres, Variational calculus with conformable fractional derivatives, arXiv:1606.07504 [math.OC]. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.