Abstract
Using the first integral method (FIM) and the functional variable method (FVM), firstly we find the analytical solutions of conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE) and finally, we present numerical results in tables and charts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability statement
This manuscript has no associated data.
References
Arshed, S., Biswas, A., Alzahrani, A.K., Belic, M.R.: Solitons in nonlinear directional couplers with optical metamaterials by first integral method. Optik 218, 1–16 (2020)
Chen, S.-B., Rashid, S., Noor, M.A., Hammouch, Z., Chu, Y.-M.: New fractional approaches for n-polynomial P -convexity with applications in special function theory. Adv. Difference Equ. 1(543), 1–31 (2020)
Chen, S.-B., Rashid, S., Noor, M.A., Ashraf, R., Chu, Y.-M.: A new approach on fractional calculus and probability density function. AIMS Math. 5(6), 1–7 (2020)
Chu, Y.-M., Nazir, U., Sohail, M., Selim, M.M., Lee, J.-R.: Enhancement in thermal energy and solute particles using hybrid nanoparticles by engaging activation energy and chemical reaction over a parabolic surface via finite element approach. Fractal Fract. 5(3), 1–17 (2021)
Darvishi, M.T., Najafi, M., Wazwaz, A.M.: Some optical soliton solutions of space-time conformable fractional Schrödinger-type models. Phys. Scr. 96(6), 1–8 (2021)
Duran, S.: Solitary wave solutions of the coupled Konno-Oono equation by using the functional variable method and the two variables (G’/G, 1/G)-expansion method. Adıyaman Univ. J. Sci. 10(2), 585–594 (2020)
Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space-time fractional Schrödinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation. Opt. Quant. Electron. 49(8), 1–15 (2017)
Ghosh, A., Maitra, S.: The first integral method and some nonlinear models. Comput. Appl. Math. 40(3), 1–16 (2021)
Jahanshahi, H., Orozco-López, O., Munoz-Pacheco, J.M., Alotaibi, N.D., Volos, C., Wang, Z., Chu, Y.M.: Simulation and experimental validation of a non-equilibrium chaotic system. Chaos, Solitons Fractals 143, 1–11 (2021)
Karthikeyan, K., Karthikeyan, P., Baskonus, H.M., Venkatachalam, K., Chu, Y.-M.: Almost sectorial operators on \(\psi \)-Hilfer derivative fractional impulsive integro-differential equations. Math. Methods Appl. Sci. 1, 1–11 (2021)
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
Rashid, S., Sultana, S., Karaca, Y., Khalid, A., Chu, Y.-M.: Some further extensions considering discrete proportional fractional operators. Fractals 30(1), 1–12 (2022)
Rezazadeh, H., Mirhosseini-Alizamini, S.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation. Optik 172, 545–553 (2018)
Rezazadeh, H., Vahidi, J., Zafar, A., Bekir, A.: The functional variable method to find new exact solutions of the nonlinear evolution equations with dual-power-law nonlinearity. Int. J. Nonlinear Sci. Numer. Simul. 21(3–4), 249–257 (2020)
Shen, Z.-H., Chu, Y.-M., Khan, M.A., Muhammad, S., AlHartomy, O.A., Higazy, M.: Mathematical modeling and optimal control of the COVID-19 dynamics. Results Phy. 31, 1–9 (2021)
Wang, M.-K., Hong, M.-Y., Xu, Y.-F., Shen, Z.-H., Chu, Y.-M.: Inequalities for generalized trigonometric and hyperbolic functions with one parameter. J. Math. Inequal. 1, 1–12 (2020)
Xu, H.-Z., Qian, W.-M., Chu, Y.-M.: Sharp bounds for the Lemniscatic mean by the one-parameter geometric and quadratic means. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 116(1), 1–15 (2022)
Younas, U., Younis, M., Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S., Sayed, S.: Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative. Results Phys. 20, 1–10 (2021)
Zhou, S.S., Jahanshahi, H., Din, Q., Bekiros, S., Alcaraz, R., Alassafi, M.O., Chu, Y.M.: Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control. Chaos, Solitons & Fractals 142, 1–11 (2021)
Acknowledgements
José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Contributions
SRA Conceptualization, Methodology, Writing-Original draft, Supervision; RS Conceptualization, Methodology, Writing-Original draft preparation; JV Validation, Formal analysis, Investigation; JFG-A Conceptualization, Methodology, Writing-Original draft preparation, Supervision. All authors read and approved the final manuscript.
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aderyani, S.R., Saadati, R., Vahidi, J. et al. The exact solutions of conformable time-fractional modified nonlinear Schrödinger equation by first integral method and functional variable method. Opt Quant Electron 54, 218 (2022). https://doi.org/10.1007/s11082-022-03605-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-03605-y