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

[2] HerrmannR., Fractional Calculus: An Introduction for Physicists (World Scientific, 2011).

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

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

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

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

[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., 2015, 115: 180403.

[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, 2016, 24: 14406-14418.

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

[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, 2017, 25: 32560-32569.

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

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

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

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

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

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

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

[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., 2010, 6: 192-195.

[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., 2009, 103: 093902.

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

[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., 2016, 10: 177-213.

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

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

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

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

[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., 2016, 10: 526-531.

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

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

[29] YangJ., Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 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., 2018, 121: 023905.

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

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

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