[1] N. Laskin. Fractional quantum mechanics. Phys. Rev. E, 62, 3135-3145(2000).

[2] R. Herrmann. Fractional Calculus: An Introduction for Physicists(2011).

[3] N. Laskin. Fractional quantum mechanics and Lévy path integrals. Phys. Lett. A, 268, 298-305(2000).

[4] N. Laskin. Fractional Schrödinger equation. Phys. Rev. E, 66, 056108(2002).

[5] B. A. Stickler. Potential condensed-matter realization of space-fractional quantum mechanics: the one-dimensional Lévy crystal. Phys. Rev. E, 88, 012120(2013).

[6] S. Longhi. Fractional Schrödinger equation in optics. Opt. Lett., 40, 1117-1120(2015).

[7] Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang, M. Xiao. Propagation dynamics of a light beam in a fractional Schrödinger equation. Phys. Rev. Lett., 115, 180403(2015).

[8] L. Zhang, C. Li, H. Zhong, C. Xu, D. Lei, Y. Li, D. Fan. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes. Opt. Express, 24, 14406-14418(2016).

[9] C. Huang, L. Dong. Beam propagation management in a fractional Schrödinger equation. Sci. Rep., 7, 5442(2017).

[10] X. Huang, X. Shi, Z. Deng, Y. Bai, X. Fu. Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation. Opt. Express, 25, 32560-32569(2017).

[11] Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, M. Xiao. Diffraction-free beams in fractional Schrödinger equation. Sci. Rep., 6, 23645(2016).

[12] B. Guo, D. Huang. Existence and stability of standing waves for nonlinear fractional Schrödinger equations. J. Math. Phys., 53, 083702(2012).

[13] Q. Li, X. Wu. Soliton solutions for fractional Schrödinger equations. Appl. Math. Lett., 53, 119-124(2016).

[14] Y. Wan, Z. Wang. Bound state for fractional Schrödinger equation with saturable nonlinearity. Appl. Math. Comput., 273, 735-740(2016).

[15] C. Huang, L. Dong. Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice. Opt. Lett., 41, 5636-5639(2016).

[16] J. Xiao, Z. Tian, C. Huang, L. Dong. Surface gap solitons in a nonlinear fractional Schrödinger equation. Opt. Express, 26, 2650-2658(2018).

[17] C. M. Bender, S. Boettcher. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 80, 5243-5246(1998).

[18] C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, D. Kip. Observation of parity-time symmetry in optics. Nat. Phys., 6, 192-195(2010).

[19] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, G. Siviloglou, D. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009).

[20] K. G. Makris, R. El-Ganainy, D. N. Christodoulides, Z. H. Musslimani. Beam dynamics in PT-symmetric optical lattices. Phys. Rev. Lett., 100, 103904(2008).

[21] S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, Y. S. Kivshar. Nonlinear switching and solitons in PT-symmetric photonic systems. Laser Photon. Rev., 10, 177-213(2016).

[22] X. K. Yao, X. M. Liu. Beam dynamics in disordered PT-symmetric optical lattices based on eigenstate analyses. Phys. Rev. A, 95, 033804(2017).

[23] K. G. Makris, R. El-Ganainy, D. N. Christodoulides, Z. H. Musslimani. PT-symmetric optical lattices. Phys. Rev. A, 81, 063807(2010).

[24] Z. H. Musslimani, K. G. Makris, R. El-Ganainy, D. N. Christodoulides. Optical solitons in PT periodic potentials. Phys. Rev. Lett., 100, 030402(2008).

[25] Y. V. Kartashov, C. Hang, G. Huang, L. Torner. Three-dimensional topological solitons in PT-symmetric optical lattices. Optica, 3, 1048-1055(2016).

[26] Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, M. Xiao. PT symmetry in a fractional Schrödinger equation. Laser Photon. Rev., 10, 526-531(2016).

[27] L. Dong, C. Huang. Double-hump solitons in fractional dimensions with a PT-symmetric potential. Opt. Express, 26, 10509-10518(2018).

[28] J. Yang, T. I. Lakoba. Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations. Stud. Appl. Math., 118, 153-197(2007).

[29] J. Yang. Nonlinear Waves in Integrable and Nonintegrable Systems(2010).

[30] X. M. Liu, X. K. Yao, Y. D. Cui. Real-time dynamics of the build-up of solitons in mode-locked lasers. Phys. Rev. Lett., 121, 023905(2018).

[31] Y. Lumer, Y. Plotnik, M. C. Rechtsman, M. Segev. Nonlinearly induced PT transition in photonic systems. Phys. Rev. Lett., 111, 263901(2013).

[32] S. Nixon, L. Ge, J. Yang. Stability analysis for solitons in PT-symmetric optical lattices. Phys. Rev. A, 85, 023822(2012).

[33] J. Yang. Iteration methods for stability spectra of solitary waves. J. Comput. Phys., 227, 6862-6876(2008).