New solutions to the fractional perturbed Chen–Lee–Liu equation with a new local fractional derivative

References

• Javid A, Raza N. Singular and dark optical solitons to the well posed Lakshmanan–Porsezian–Daniel model. Optik. 2018;171:120–129.
   Web of Science ®Google Scholar
• Afzal U, Raza N, Murtaza IG. On soliton solutions of time fractional form of Sawada–Kotera equation. Nonlinear Dyn. 2019;95(1):391–405.
   Web of Science ®Google Scholar
• Arshed S, Raza N. Optical solitons perturbation of Fokas–Lenells equation with full nonlinearity and dual dispersion. Chin J Phys. 2020;63:314–324.
   Web of Science ®Google Scholar
• Kaplan M, Hosseini K, Samadani F, et al. Optical soliton solutions of the cubic-quintic non-linear Schrodinger equation including an anti-cubic term. J Mod Opt. 2018;65(12):1431–1436.
   Web of Science ®Google Scholar
• Vahidi J, Zekavatmand SM, Rezazadeh H, et al. New solitary wave solutions to the coupled Maccaris system. Results Phys. 2021;21:103801.
   Web of Science ®Google Scholar
• Rezazadeh H, Inc M, Baleanu D. New solitary wave solutions for variants of (3+1)-dimensional Wazwaz–Benjamin–Bona–Mahony equations. Front Phys. 2020;8:332.
   Web of Science ®Google Scholar
• Manafian J, Ilhan OA, Alizadeh AA. Periodic wave solutions and stability analysis for the KP-BBM equation with abundant novel interaction solutions. Phys Scr. 2020;95(6):065203.
   Web of Science ®Google Scholar
• Manafian J. Novel solitary wave solutions for the (3+1)-dimensional extended Jimbo-Miwa equations. Comput Math Appl. 2018;76(5):1246–1260.
   Web of Science ®Google Scholar
• Ilhan OA, Manafian J, Shahriari M. Lump wave solutions and the interaction phenomenon for a variable-coefficient Kadomtsev-Petviashvili equation. Comput Math Appl. 2019;78(8):2429–2448.
   Web of Science ®Google Scholar
• Pashayi S, Hashemi MS, Shahmorad S. Analytical lie group approach for solving fractional integro-differential equations. Commun Nonlinear Sci Numer Simul. 2017;51:66–77.
   Web of Science ®Google Scholar
• Rezazadeh H, Korkmaz A, Khater MM, et al. New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method. Mod Phys Lett B. 2019;33(28):1950338.
   Web of Science ®Google Scholar
• Rezazadeh H, Osman MS, Eslami M, et al. Mitigating internet bottleneck with fractional temporal evolution of optical solitons having quadratic-cubic nonlinearity. Optik. 2018;164:84–92.
   Web of Science ®Google Scholar
• Pinar Z, Rezazadeh H, Eslami M. Generalized logistic equation method for Kerr law and dual power law Schrödinger equations. Opt Quant Elec. 2020;52(12):1–16.
   Web of Science ®Google Scholar
• Khater MM, Seadawy AR, Lu D. New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel (G'/G)-expansion method. Pramana. 2018;90(5):59.
   Web of Science ®Google Scholar
• Jhangeer A, Hussain A, Junaid-U-Rehman M, et al. Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation. Chaos Solitons Fractals. 2021;143:110578.
   Web of Science ®Google Scholar
• Hussain A, Jhangeer A, Abbas N, et al. Optical solitons of fractional complex Ginzburg Landau equation with conformable, beta, and M-truncated derivatives: a comparative study. Adv Differ Equ. 2020;2020(1):1–19.
   PubMed Web of Science ®Google Scholar
• Jhangeer A, Rezazadeh H, Abazari R, et al. Lie analysis, conserved quantities and solitonic structures of Calogero–Degasperis–Fokas equation. Alex Eng J. 2021;60(2):2513–2523.
   Web of Science ®Google Scholar
• Hashemi MS, Akgül A. Solitary wave solutions of time-space nonlinear fractional Schrödinger equation: two analytical approaches. J Comput Appl Math. 2018;339:147–160.
   Web of Science ®Google Scholar
• Najafi R, Bahrami F, Hashemi MS. Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations. Nonlinear Dyn. 2017;87(3):1785–1796.
   Web of Science ®Google Scholar
• Korpinar Z, Inc M, Bayram M, et al. New optical solitons for Biswas–Arshed equation with higher order dispersions and full nonlinearity. Optik. 2020;206:163332.
   Web of Science ®Google Scholar
• Abdelrahman MA, Hassan SZ, Inc M. The coupled nonlinear Schrödinger-type equations. Mod Phys Lett B. 2020;34(06):2050078.
   Google Scholar
• Ghanbari B. Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative. Math Methods Appl Sci. 2021. doi:10.1002/mma.7302.
   Google Scholar
• Srivastava HM, Günerhan H, Ghanbari B. Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity. Math Methods Appl Sci. 2019;42(18):7210–7221.
   Web of Science ®Google Scholar
• Ghanbari B, Nisar KS, Aldhaifallah M. Abundant solitary wave solutions to an extended nonlinear Schrodinger equation with conformable derivative using an efficient integration method. Adv Differ Equ. 2020;2020(1):1–25.
   PubMed Web of Science ®Google Scholar
• Ghanbari B. On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique. Math Methods Appl Sci. 2021;44(6):4673–4685.
   Web of Science ®Google Scholar
• Hosseini K, Mirzazadeh M, Gomez-Aguilar JF. Soliton solutions of the Sasa-Satsuma equation in the monomode optical fibers including the beta-derivatives. Optik. 2020;224:165425.
   Web of Science ®Google Scholar
• Hosseini K, Mirzazadeh M, Vahidi J, et al. Optical wave structures to the Fokas–Lenells equation. Optik. 2020;207:164450.
   Web of Science ®Google Scholar
• Hosseini K, Mirzazadeh M, Ilie M, et al. Dynamics of optical solitons in the perturbed Gerdjikov–Ivanov equation. Optik. 2020;206:164350.
   Web of Science ®Google Scholar
• Osman MS, Rezazadeh H, Eslami M, et al. Analytical study of solitons to Benjamin–Bona–Mahony–Peregrine equation with power law nonlinearity by using three methods. Univ Politeh Buch Sci Bull Ser A-Appl Math Phys. 2018;80(4):267–278.
   Google Scholar
• Bansal A, Biswas A, Zhou Q, et al. Optical solitons with Chen–Lee–Liu equation by Lie symmetry. Phys Lett A. 2020;384(109):126202.
   Google Scholar
• Biswas A, Ekici M, Sonmezoglu A, et al. Chirped optical solitons of Chen–Lee–Liu equation by extended trial equation scheme. Optik. 2018;156:999–1006.
   Web of Science ®Google Scholar
• Biswas A. Chirp-free bright optical soliton perturbation with Chen–Lee–Liu equation by traveling wave hypothesis and semi-inverse variational principle. Optik. 2018;172:772–776.
   Web of Science ®Google Scholar
• Chow KW, Ng TW. Periodic solutions of a derivative nonlinear Schrödinger equation: elliptic integrals of the third kind. J Comput Appl Math. 2011;235:3825–3830.
   Web of Science ®Google Scholar
• Jawad AJM, Biswas A, Zhou Q, et al. Chirped singular and combo optical solitons for Chen–Lee–Liu equation with three forms of integration architecture. Optik. 2019;178:172–177.
   Web of Science ®Google Scholar
• Kara AH, Biswas A, Zhou Q, et al. Conservation laws for optical solitons with Chen–Lee–Liu equation. Optik. 2018;174:195–198.
   Web of Science ®Google Scholar
• Kudryashov NA. General solution of the traveling wave reduction for the perturbed Chen–Lee–Liu equation. Optik. 2019;186:339–349.
   Web of Science ®Google Scholar
• Mohammed ASHF, Bakodah HO, Banaja MA, et al. Bright optical solitons of Chen–Lee–Liu equation with improved Adomian decomposition method. Optik. 2019;181:964–970.
   Web of Science ®Google Scholar
• Moses J, Wise FW. Self-steepening without self-phase modulation. In: IEEE quantum electronics and laser science conference. Baltimore (MD); 2007. p.1–2
   Google Scholar
• Triki H, Babatin MM, Biswas A. Chirped bright solitons for Chen–Lee–Liu equation in optical fibers and PCF. Optik. 2017;149:300–303.
   Web of Science ®Google Scholar
• Triki H, Hamaizi Y, Zhou Q, et al. Chirped dark and gray solitons for Chen–Lee–Liu equation in optical fibers and PCF. Optik. 2018;155:329–333.
   Web of Science ®Google Scholar
• Triki H, Hamaizi Y, Zhou Q, et al. Chirped singular solitons for Chen–Lee–Liu equation in optical fibers and PCF. Optik. 2018;157:156–160.
   Web of Science ®Google Scholar
• Xia J-W, Zhao Y-W, Lü X. Predictability, fast calculation and simulation for the interaction solutions to the cylindrical Kadomtsev-Petviashvili equation. Commun Nonlinear Sci Numer Simul. 2020;90:105260.
   Web of Science ®Google Scholar
• Lü X, Chen S-J. Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dyn. 2021;103:947–977.
   Web of Science ®Google Scholar
• Xu H-N, Ruan W-Y, Zhang Y, et al. Multi-exponential wave solutions to two extended Jimbo–Miwa equations and the resonance behavior. Appl Math Lett. 2020;99:105976.
   Web of Science ®Google Scholar
• Hossen MB, Roshid H-O, Zulfikar Ali M. Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2+1)-dimensional breaking soliton equation. Phys Lett A. 2018;382:1268–1274.
   Web of Science ®Google Scholar
• Ullah MS, Zulfikar Ali M, Roshid H-O, et al. Collision phenomena among lump, periodic and soliton solutions to a (2+1)-dimensional Bogoyavlenskii's breaking soliton model. Phys Lett A. 2021;397:127263.
   Web of Science ®Google Scholar
• Ma W-X. Complexiton solutions to the Korteweg–de Vires equation. Phys Lett A. 2002;301(1–2):35–44.
   Web of Science ®Google Scholar
• Khatun MS, Hoque MF, Rahman MA. Multisoliton solutions, completely elastic collisions and non-elastic fusion phenomena of two PDEs. Pramana-J Phys. 2017;88:86.
   Web of Science ®Google Scholar
• Roshid H-O, Rashidi MM. Multi-soliton fusion phenomenon of Burgers equation and fission, fusion phenomenon of Sharma–Tasso–Olver equation. J Ocean Eng Sci. 2017;2(2):120–126.
   Web of Science ®Google Scholar
• Lü X, Hua Y-F, Chen S-J, et al. Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painlevé analysis, soliton solutions, Bäcklund transformation, Lax pair and infinitely many conservation laws. Commun Nonlinear Sci Numer Simul. 2021;95:105612.
   Web of Science ®Google Scholar
• Yin Y-H, Chen S-J, Lü X. Localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations. Chin Phys B. 2020;29:120502.
   Web of Science ®Google Scholar
• Chen S-J, Lü X, Tang X-F. Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients. Commun Nonlinear Sci Numer Simul. 2021;95:105628.
   Web of Science ®Google Scholar
• Lü X, Ma W-X. Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dyn. 2016;85:1217–1222.
   Web of Science ®Google Scholar
• Chen S-J, Lü X, Ma W-X. Predictability, fast calculation and simulation for the interaction solutions to the cylindrical Kadomtsev–Petviashvili equation. Commun Nonlinear Sci Numer Simul. 2020;83:105135.
   Web of Science ®Google Scholar
• Roshid H-O, Khan MH, Wazwaz A-M. Lump, multi-lump, cross kinky-lump and manifold periodic-soliton solutions for the (2+1)-D Calogero–Bogoyavlenskii–Schiff equation. Heliyon. 2020;6:e03701.
   PubMed Web of Science ®Google Scholar
• He X-J, Lü X, Li M-G. Predictability, fast calculation and simulation for the interaction solutions to the cylindrical Kadomtsev–Petviashvili equation. Anal Math Phys. 2020;11:4.
   Google Scholar
• Roshid H-O, Kabir MR, Bhowmik RC, et al. Investigation of solitary wave solutions for Vakhnenko–Parkes equation via exp-function and exp (−φ(ξ))-expansion method. SpringerPlus. 2014;3:692.
   PubMedGoogle Scholar
• Roshid H-O, Rahman MA. The exp (−Φ(ξ))-expansion method with application in the (1+1)-dimensional classical Boussinesq equations. Res Phys. 2014;4:150–155.
   Google Scholar
• Hossen MB, Roshid H-O, Zulfikar Ali M. Modified double sub-equation method for finding complexiton solutions to the (1+1) dimensional nonlinear evolution equations. Int J Appl Comput Math. 2017;3:679–697.
   Google Scholar
• Roshid H-O. Novel solitary wave solution in shallow water and ion acoustic plasma waves in-terms of two nonlinear models via MSE method. J Ocean Eng Sci. 2017;2(2):196–202.
   Google Scholar
• Yıldırım Y, Biswas A, Asma M, et al. Optical soliton perturbation with Chen–Lee–Liu equation. Optik. 2020;220:165177.
   Web of Science ®Google Scholar
• Khalil R, Horani MA, Yousef A, et al. A new definition of fractional derivative. J Comput Appl Math. 2014;264:65–70.
   Web of Science ®Google Scholar
• Guzman PM, Langton G, Motta Bittencurt LML, et al. A new definition of a fractional derivative of local type. J Math Anal. 2018;9(2):88–98.
   Web of Science ®Google Scholar
• Almeida R, Guzowska M, Odzijewicz T. A remark on local fractional calculus and ordinary derivatives. Open Math. 2016;14:1122–1124.
   Web of Science ®Google Scholar
• Abdeljawad T. On conformable fractional calculus. J Comput Appl Math. 2015;279:57–66.
   Web of Science ®Google Scholar
• Sousa JVDC, de Oliveira EC. A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties. Int J Anal Appl. 2018;16(1):83–96.
   Google Scholar
• Ivanov SK. Riemann problem for the light pulses in optical fibers for the generalized Chen–Lee–Liu equation. Phys Rev A. 2020;101:053827.
   Web of Science ®Google Scholar
• Gennady A El, Geogjaev VV, Gurevich AV, et al. Decay of an initial discontinuity in the defocusing NLS hydrodynamics. Phys D. 1995;87:186–192.
   Google Scholar
• Fujioka J, Cortés E, Pérez-Pascual R, et al. Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management. Chaos. 2011;21:033120.
   PubMed Web of Science ®Google Scholar
• Seadawy AR, Lu D, Nasreen N, et al. Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity and modulation instability analysis. Phys A. 2019;534:122155.
   Web of Science ®Google Scholar
• Zhang ZY, Liu ZH, Miao XJ, et al. New exact solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. Appl Math Comput. 2010;216:3064–3072.
   Web of Science ®Google Scholar
• Yépez-Martínez H, Gómez-Aguilar JF. M-derivative applied to the dispersive optical solitons for the Schrödinger–Hirota equation. Eur Phys J Plus. 2019;134:1–10.
   Web of Science ®Google Scholar
• Yıldırım Y. Optical solitons to Chen–Lee–Liu model in birefringent fibers with modified simple equation approach. Optik. 2019;183:612–618.
   Web of Science ®Google Scholar