[1] [1] LAUGHLIN R B. Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations[J]. Physical Review Letters, 1983, 50(18): 1395-1398. DOI: 10.1103/PhysRevLett.50.1395.

[2] [2] WEN J, ZHANG Y, XIAO M. The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics[J]. Advances in Optics & Photonics, 2013, 5(1): 83-130. DOI: 10.1364/AOP.5.000083.

[3] [3] ROKHINSON L P, LIU X, FURDYNA J K. The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles[J]. Nature Physics, 2012, 8(11): 795-799. DOI: 10.1038/nphys2429.

[4] [4] OLIVAR-ROMERO F, ROSAS-ORTIZ O. Factorization of the Quantum Fractional Oscillator[J]. Journal of Physics Conference Series, 2016, 698: 012025. DOI: 10.1088/1742-6596/698/1/012025.

[5] [5] LASKIN N. Fractional Quantum Mechanics and Lévy Path Integrals[J]. Physics Letters A, 2000, 268(4-6): 298-305. DOI: 10.1016/s0375-9601(00)00201-2.

[6] [6] LASKIN N. Fractional quantum mechanics[J]. Physical Review E, 2000, 62(3): 3135-3145. DOI: 10.1103/PhysRevE.62.3135.

[7] [7] LASKIN N. Fractional Schrdinger equation[J]. Physical Review E, 2002, 66(5): 056108. DOI: 10.1103/PhysRevE.66.056108.

[8] [8] PERTSCH T, DANNBERG P, ELFLEIN W, et al. Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays[J]. Physical Review Letters, 1999, 83(23): 4752-4755. DOI: 10.1103/PhysRevLett.83.4752.

[9] [9] CHREMMOS I D, EFREMIDIS N K. Surface optical Bloch oscillations in semi-infinite waveguide arrays[J]. Optics Letters, 2012, 37(11): 1892-1894. DOI: 10.1364/OL.37.001892.

[10] [10] ZHANG Y, ZHANG D, ZHANG Z, et al. Optical Bloch oscillation and Zener tunneling in an atomic system[J]. Optica, 2017, 4(5): 571. DOI: 10.1364/OPTICA.4.000571.

[11] [11] FANG W Y, KARTASHOV Y V, HU B, et al. Twin-vortex solitons in nonlocal nonlinear media[J]. Optics Letters, 2010, 35(5): 628-630. DOI: 10.1364/OL.35.000628.

[12] [12] CHEN L, WANG Q, SHEN M, et al. Nonlocal dark solitons under competing cubic-quintic nonlinearities[J]. Optics Letters, 2013, 38(1): 13-15. DOI: 10.1364/OL.38.000013.

[13] [13] ZHANG H F, XU F, ZHU D S, et al. Soliton controlling and steering in asymmetric nonlocal media with optical lattices[J]. Optics Express, 2014, 22(1): 995-1007. DOI: 10.1364/OE.22.000995.

[14] [14] FLEISCHER J W, SEGEV M, EFREMIDIS N K, et al. Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices[J]. Nature, 2003, 422(6928): 147-150. DOI: 10.1038/nature01452.

[15] [15] CHRISTODOULIDES D N, LEDERER F, SILBERBERG Y. Discretizing light behaviour in linear and nonlinear waveguide lattices[J]. Nature, 2003, 424(6950): 817-823. DOI: 10.1038/nature01936.

[16] [16] IWANOW R, SCHIEK R, STEGEMAN G I, et al. Observation of Discrete Quadratic Solitons[J]. Physical Review Letters, 2004, 93(11): 5508. DOI: 10.1103/PhysRevLett.93.113902.

[17] [17] MAI Z, FU S, WU J, et al. Discrete solitons in waveguide arrays with long-range linearly coupled effect[J]. Journal of the Physical Society of Japan, 2014, 83(3): 2687-2688. DOI: 10.7566/JPSJ.83.034404.

[18] [18] MEIER J, STEGEMAN G I, CHRISTODOULIDES D N, et al. Experimental Observation of Discrete Modulational Instability[J]. Physical Review Letters, 2004, 92(16): 163902. DOI: 10.1103/PhysRevLett.92.163902.

[19] [19] YE F, MIHALACHE D, HU B, et al. Subwavelength Plasmonic Lattice Solitons in Arrays of Metallic Nanowires[J]. Physical Review Letters, 2010, 104(10): 106802. DOI: 10.1103/PhysRevLett.104.106802.

[20] [20] YE F, MIHALACHE D, HU B, et al. Subwavelength vortical plasmonic lattice solitons[J]. Optics Letters, 2011, 36(7): 1179-1181. DOI: 10.1364/OL.36.001179.

[22] [22] MAKRIS K G, EL-GANAINY R, CHRISTODOULIDES D N, et al. Beam dynamics in PT symmetric optical lattices[J]. Physical Review Letters, 2008, 100(10): 103904. DOI: 10.1103/PhysRevLett.100.103904.

[23] [23] GUO A, SALAMO G J, DUCHESNE D, et al. Observation of PT-Symmetry Breaking in Complex Optical Potentials[J]. Physical Review Letters, 2009, 103(9): 093902. DOI: 10.1103/PhysRevLett.103.093902.

[24] [24] KARTASHOV Y V, VYSLOUKH V A, TORNER L. Resonant Mode Oscillations in Modulated Waveguiding Structures[J]. Physical Review Letters, 2007, 99(23): 233903. DOI: 10.1103/PhysRevLett.99.233903.

[25] [25] SHANDAROVA K, RUETER C E, KIP D, et al. Experimental Observation of Rabi Oscillations in Photonic Lattices[J]. Physical Review Letters, 2009, 102(12): 123905. DOI: 10.1103/PhysRevLett.102.123905.

[26] [26] LONGHI S. Fractional Schrdinger equation in optics[J]. Optics Letters, 2015, 40(6): 1117. DOI: 10.1364/OL.40.001117.

[30] [30] ZHANG Y Q, WANG R, ZHONG H, et al. Optical Bloch oscillation and Zener tunneling in the fractional Schrdinger equation[J]. Scientific Reports, 2017, 7(1): 17872. DOI: 10.1038/s41598-017-17995-7.

[31] [31] ANDR L, ALWIN K. Fractional Schrdinger Equation in the Presence of the Linear Potential[J]. Mathematics, 2016, 4(2): 31. DOI: 10.3390/math4020031.

[32] [32] ZHANG L, LI C, ZHONG H, et al. Propagation dynamics of super-Gaussian beams in fractional Schrdinger equation: from linear to nonlinear regimes[J]. Optics Express, 2016, 24(13): 14406-14418. DOI:10.1364/OE.24.014406.

[33] [33] HUANG C, DONG L. Gap solitons in the nonlinear fractional Schrdinger equation with an optical lattice[J]. Optics Letters, 2016, 41(24): 5636. DOI: 10.1364/OL.41.005636.

[34] [34] DONG L, HUANG C. Double-hump solitons in fractional dimensions with a PT symmetric potential[J]. Optics Express, 2018, 26(8): 10509. DOI: 10.1364/OE.26.010509.

[35] [35] OWYED S, ABDOU M A, ABDEL-ATY A, et al. Optical solitons solutions for perturbed time fractional nonlinear Schrdinger equation via two strategic algorithms[J]. AIMS Mathematics, 2020, 5(3): 2057-2070. DOI: 10.3934/math.2020136.

[36] [36] RAY S S. Dispersive optical solitons of time-fractional Schrdinger-Hirota equation in nonlinear optical fibers[J]. Physica A: Statistical Mechanics and its Applications, 2019, 537(4): 122619. DOI: 10.1016/j.physa.2019.122619.

[37] [37] LI P, LI R, DAI C. Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction[J]. Optics Express, 2021, 29(3): 3193-3210. DOI: 10.1364/OE.415028.