C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation with an optical lattice,” Sci. Rep. 7, 5442 (2017).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

W.-P. Zhong, M. R. Belić, and Y. Zhang, “Accessible solitons of fractional dimension,” Ann. Phys. 368, 110–116 (2016).

[Crossref]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

F. Olivar-Romero and O. Rosas-Ortiz, “Factorization of the quantum fractional oscillator,” J. Phys.: Condens. Matter. 698, 012025 (2016).

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

[Crossref]

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

[Crossref]
[PubMed]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]
[PubMed]

S. Longhi, “Fractional Schrödinger equation in optics,” Opt. Lett. 40, 1117–1120 (2015).

[Crossref]
[PubMed]

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

[Crossref]

M. Żaba and P. Garbaczewski, “Solving fractional schrödinger-type spectral problems: Cauchy oscillator and Cauchy well,” J. Math. Phys. 55, 092103 (2014).

[Crossref]

H. Liu, H. Jin, and L. Dong, “Disordered surface gap solitons,” Phys. Rev. A 89, 023826 (2014).

[Crossref]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).

[Crossref]

Y. Luchko, “Fractional Schrödinger equation for a particle moving in a potential well,” J. Math. Phys. 54, 012111 (2013).

[Crossref]

A. Kundu and B. Seradjeh, “Transport signatures of Floquet majorana fermions in driven topological superconductors,” Phys. Rev. Lett. 111, 136402 (2013).

[Crossref]
[PubMed]

B. A. Stickler, “Potential condensed-matter realization of space-fractional quantum mechanics: The one-dimensional lévy crystal,” Phys. Rev. E 88, 012120 (2013).

[Crossref]

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

[Crossref]

J. Lőrinczi and J. Małecki, “Spectral properties of the massless relativistic harmonic oscillator,” J. Differ. Equations 253, 2846–2871 (2012).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in pt-symmetric optical lattices,” Opt. Lett. 37, 4543–4545 (2012).

[Crossref]
[PubMed]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).

[Crossref]

J. Dong and M. Xu, “Some solutions to the space fractional Schrödinger equation using momentum representation method,” J. Math. Phys. 48, 072105 (2007).

[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).

[Crossref]
[PubMed]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14, 4808 (2006).

[Crossref]
[PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271 (2006).

[Crossref]
[PubMed]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[Crossref]
[PubMed]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66, 056108 (2002).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268, 298–305 (2000).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62, 3135–3145 (2000).

[Crossref]

R. B. Laughlin, “Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations,” Phys. Rev. Lett. 50, 1395–1398 (1983).

[Crossref]

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

[Crossref]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).

[Crossref]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[Crossref]
[PubMed]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

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

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

W.-P. Zhong, M. R. Belić, and Y. Zhang, “Accessible solitons of fractional dimension,” Ann. Phys. 368, 110–116 (2016).

[Crossref]

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

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

J. Dong and M. Xu, “Some solutions to the space fractional Schrödinger equation using momentum representation method,” J. Math. Phys. 48, 072105 (2007).

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation with an optical lattice,” Sci. Rep. 7, 5442 (2017).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]
[PubMed]

H. Liu, H. Jin, and L. Dong, “Disordered surface gap solitons,” Phys. Rev. A 89, 023826 (2014).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in pt-symmetric optical lattices,” Opt. Lett. 37, 4543–4545 (2012).

[Crossref]
[PubMed]

M. Żaba and P. Garbaczewski, “Solving fractional schrödinger-type spectral problems: Cauchy oscillator and Cauchy well,” J. Math. Phys. 55, 092103 (2014).

[Crossref]

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

[Crossref]

R. Herrmann, Fractional Calculus: An Introduction for Physicists (World Scientific, 2001).

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation with an optical lattice,” Sci. Rep. 7, 5442 (2017).

[Crossref]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]
[PubMed]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in pt-symmetric optical lattices,” Opt. Lett. 37, 4543–4545 (2012).

[Crossref]
[PubMed]

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

[Crossref]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

H. Liu, H. Jin, and L. Dong, “Disordered surface gap solitons,” Phys. Rev. A 89, 023826 (2014).

[Crossref]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14, 4808 (2006).

[Crossref]
[PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).

[Crossref]
[PubMed]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).

[Crossref]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[Crossref]
[PubMed]

A. Kundu and B. Seradjeh, “Transport signatures of Floquet majorana fermions in driven topological superconductors,” Phys. Rev. Lett. 111, 136402 (2013).

[Crossref]
[PubMed]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66, 056108 (2002).

[Crossref]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268, 298–305 (2000).

[Crossref]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62, 3135–3145 (2000).

[Crossref]

R. B. Laughlin, “Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations,” Phys. Rev. Lett. 50, 1395–1398 (1983).

[Crossref]

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

[Crossref]
[PubMed]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in pt-symmetric optical lattices,” Opt. Lett. 37, 4543–4545 (2012).

[Crossref]
[PubMed]

H. Liu, H. Jin, and L. Dong, “Disordered surface gap solitons,” Phys. Rev. A 89, 023826 (2014).

[Crossref]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in pt-symmetric optical lattices,” Opt. Lett. 37, 4543–4545 (2012).

[Crossref]
[PubMed]

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

[Crossref]

J. Lőrinczi and J. Małecki, “Spectral properties of the massless relativistic harmonic oscillator,” J. Differ. Equations 253, 2846–2871 (2012).

[Crossref]

Y. Luchko, “Fractional Schrödinger equation for a particle moving in a potential well,” J. Math. Phys. 54, 012111 (2013).

[Crossref]

J. Lőrinczi and J. Małecki, “Spectral properties of the massless relativistic harmonic oscillator,” J. Differ. Equations 253, 2846–2871 (2012).

[Crossref]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

F. Olivar-Romero and O. Rosas-Ortiz, “Factorization of the quantum fractional oscillator,” J. Phys.: Condens. Matter. 698, 012025 (2016).

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[Crossref]
[PubMed]

H. E. Ponath and G. I. Stegeman, Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).

F. Olivar-Romero and O. Rosas-Ortiz, “Factorization of the quantum fractional oscillator,” J. Phys.: Condens. Matter. 698, 012025 (2016).

A. Kundu and B. Seradjeh, “Transport signatures of Floquet majorana fermions in driven topological superconductors,” Phys. Rev. Lett. 111, 136402 (2013).

[Crossref]
[PubMed]

H. E. Ponath and G. I. Stegeman, Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).

B. A. Stickler, “Potential condensed-matter realization of space-fractional quantum mechanics: The one-dimensional lévy crystal,” Phys. Rev. E 88, 012120 (2013).

[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).

[Crossref]
[PubMed]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14, 4808 (2006).

[Crossref]
[PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).

[Crossref]
[PubMed]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).

[Crossref]

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

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

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

[Crossref]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).

[Crossref]

J. Dong and M. Xu, “Some solutions to the space fractional Schrödinger equation using momentum representation method,” J. Math. Phys. 48, 072105 (2007).

[Crossref]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).

[Crossref]

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).

[Crossref]

M. Żaba and P. Garbaczewski, “Solving fractional schrödinger-type spectral problems: Cauchy oscillator and Cauchy well,” J. Math. Phys. 55, 092103 (2014).

[Crossref]

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

[Crossref]

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

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

W.-P. Zhong, M. R. Belić, and Y. Zhang, “Accessible solitons of fractional dimension,” Ann. Phys. 368, 110–116 (2016).

[Crossref]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

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

[Crossref]

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

[Crossref]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).

[Crossref]

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

[Crossref]
[PubMed]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

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

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

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

[Crossref]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

W.-P. Zhong, M. R. Belić, and Y. Zhang, “Accessible solitons of fractional dimension,” Ann. Phys. 368, 110–116 (2016).

[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

W.-P. Zhong, M. R. Belić, and Y. Zhang, “Accessible solitons of fractional dimension,” Ann. Phys. 368, 110–116 (2016).

[Crossref]

J. Lőrinczi and J. Małecki, “Spectral properties of the massless relativistic harmonic oscillator,” J. Differ. Equations 253, 2846–2871 (2012).

[Crossref]

J. Dong and M. Xu, “Some solutions to the space fractional Schrödinger equation using momentum representation method,” J. Math. Phys. 48, 072105 (2007).

[Crossref]

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

[Crossref]

Y. Luchko, “Fractional Schrödinger equation for a particle moving in a potential well,” J. Math. Phys. 54, 012111 (2013).

[Crossref]

M. Żaba and P. Garbaczewski, “Solving fractional schrödinger-type spectral problems: Cauchy oscillator and Cauchy well,” J. Math. Phys. 55, 092103 (2014).

[Crossref]

F. Olivar-Romero and O. Rosas-Ortiz, “Factorization of the quantum fractional oscillator,” J. Phys.: Condens. Matter. 698, 012025 (2016).

Y. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. Zhong, Y. Zhang, D. N. Christodoulides, and M. Xiao, “Pt symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).

[Crossref]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14, 4808 (2006).

[Crossref]
[PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271 (2006).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

C. Huang and L. Dong, “Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice,” Opt. Lett. 41, 5636–5639 (2016).

[Crossref]
[PubMed]

C. Li, C. Huang, H. Liu, and L. Dong, “Multipeaked gap solitons in pt-symmetric optical lattices,” Opt. Lett. 37, 4543–4545 (2012).

[Crossref]
[PubMed]

S. Longhi, “Fractional Schrödinger equation in optics,” Opt. Lett. 40, 1117–1120 (2015).

[Crossref]
[PubMed]

N. Laskin, “Fractional quantum mechanics and Lévy path integrals,” Phys. Lett. A 268, 298–305 (2000).

[Crossref]

H. Liu, H. Jin, and L. Dong, “Disordered surface gap solitons,” Phys. Rev. A 89, 023826 (2014).

[Crossref]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).

[Crossref]

B. A. Stickler, “Potential condensed-matter realization of space-fractional quantum mechanics: The one-dimensional lévy crystal,” Phys. Rev. E 88, 012120 (2013).

[Crossref]

W.-P. Zhong, M. R. Belić, B. A. Malomed, Y. Zhang, and T. Huang, “Spatiotemporal accessible solitons in fractional dimensions,” Phys. Rev. E 94, 012216 (2016).

[Crossref]
[PubMed]

N. Laskin, “Fractional quantum mechanics,” Phys. Rev. E 62, 3135–3145 (2000).

[Crossref]

N. Laskin, “Fractional Schrödinger equation,” Phys. Rev. E 66, 056108 (2002).

[Crossref]

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

[Crossref]

A. Kundu and B. Seradjeh, “Transport signatures of Floquet majorana fermions in driven topological superconductors,” Phys. Rev. Lett. 111, 136402 (2013).

[Crossref]
[PubMed]

R. B. Laughlin, “Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations,” Phys. Rev. Lett. 50, 1395–1398 (1983).

[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).

[Crossref]
[PubMed]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[Crossref]
[PubMed]

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

[Crossref]

C. Huang and L. Dong, “Beam propagation management in a fractional Schrödinger equation with an optical lattice,” Sci. Rep. 7, 5442 (2017).

[Crossref]

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010).

[Crossref]

R. Herrmann, Fractional Calculus: An Introduction for Physicists (World Scientific, 2001).

H. E. Ponath and G. I. Stegeman, Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).