References
- Al-Refai M, Jarrah AM. Fundamental results on weighted Caputo-Fabrizio fractional derivative. Chaos Solit Fractals. 2019;126:7–11. doi: 10.1016/j.chaos.2019.05.035
- Atangana A, Baleanu D. New fractional derivatives with non-local and nonsingular kernel: theory and applications to heat transfer model. J Therm Sci. 2016;20(2):763–769. doi: 10.2298/TSCI160111018A
- Abbas S, Benchohra M, Nieto J. Caputo-Fabrizio fractional differential equations with instantaneous impulses. AIMS Math. 2021;6(3):2932–2946. doi: 10.3934/math.2021177
- Hosseini K, Ilie M, Mirzazadeh M, et al. The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations. Commun Theor Phys. 2022;74(7): doi: 10.1088/1572-9494/ac633e
- Ilie M, Biazar J, Ayati Z. Analytical study of exact traveling wave solutions for time-fractional nonlinear Schrödinger equations. Opt Quantum Electron. 2018;50:413. doi: 10.1007/s11082-018-1682-y
- Eslami M, Hosseini K, Matinfar M, et al. A nonlinear Schrödinger equation describing the polarization mode and its chirped optical solitons. Opt Quantum Electron. 2021;53:314. doi: 10.1007/s11082-021-02917-9
- Ali KK, Maneea M. Optical solitons using optimal homotopy analysis method for time-fractional (1+1)-dimensional coupled nonlinear Schrodinger equations. Optik. 2023;283:Article ID 170907. doi: 10.1016/j.ijleo.2023.170907
- Ali KK, Mohamed MS, Maneea M. Exploring optical soliton solutions of the time fractional q-deformed Sinh-Gordon equation using a semi-analytic method. AIMS Math. 2023;8(11):27947–27968. doi: 10.3934/math.20231429
- Sierociuk D, Skovranek T, Macias M, et al. Diffusion process modeling by using fractional-order models. Appl Math Comput. 2015;257:2–11.
- Ray SS. Nonlinear differential equations in physics. Singapore: Springer Nature; 2020.
- Ortega JB, Sardella E, Aguiar JA. Superconducting properties of a parallelepiped mesoscopic superconductor: a comparative study between the 2D and 3D Ginzburg-Landau models. Phys Lett A. 2015;379(7):732–737. doi: 10.1016/j.physleta.2014.12.030
- Aranson IS, Kramer L. The world of the complex Ginzburg-Landau equation. Rev Mod Phys. 2002;74(1):99–143. doi: 10.1103/RevModPhys.74.99
- Yang Y, Gao H. Continuous dependence on modeling for a complex Ginzburg-Landau equation with complex coefficients. Math Meth Appl Sci. 2004;27:1567–1578. doi: 10.1002/mma.v27:13
- Gao H, Wang X. On the global existence and small dispersion limit for a class of complex Ginzburg-Landau equations. Math Meth Appl Sci. 2009;32:1396–1414. doi: 10.1002/mma.v32:11
- Park J. Bifurcation and stability of the generalized complex Ginzburg-Landau equation. Pure Appl Anal. 2008;7(5):1237–1253.
- Sherratt JA, Smith MJ, Rademacher JDM. Patterns of sources and sinks in the complex Ginzburg-Landau equation with zero linear dispersion. SIAM J Appl Dyn Syst. 2010;9(3):883–918. doi: 10.1137/090780961
- Naghshband S, Araghi MAF. Solving generalized quintic comple Ginzburg-Landau equation by homotopy analysis method. Ain Shams Eng J. 2018;9:607–613. doi: 10.1016/j.asej.2016.01.015
- Wang P, Huang C. An efficient fourth-order in space difference scheme for the nonlinear fractional GinzburgLandau equation. BIT Numer Math. 2018;58(3):783–805. doi: 10.1007/s10543-018-0698-9
- Wang N, Huang C. An efficient split-step quasicompact finite difference method for the nonlinear fractional Ginzburg-Landau equations. Comput Math Appl. 2018;75(7):2223–2242. doi: 10.1016/j.camwa.2017.12.005
- Hosseini K, Mirzazadeh M, Osman MS, et al. Solitons and Jacobi elliptic function solutions to the complex Ginzburg-Landau equation. Front Phys. 2020;8:225. doi: 10.3389/fphy.2020.00225
- Arshed S, Raza N, Rahman RU, et al. Sensitive behavior and optical solitons of complex fractional Ginzburg-Landau equation: a comparative paradigm. Results Phys. 2021;28:Article ID 104533. doi: 10.1016/j.rinp.2021.104533
- Yao S, Ilhan E, Veeresha P, et al. A powerful iterative approach for quintic complex ginzburglandau equation within the frame of fractional operator. Fractals. 2021;29(5):Article ID 2140023. doi: 10.1142/S0218348X21400235
- Ouahid L, Abdou MA, Owyed S, et al. New optical solitons for complex Ginzburg-Landau equation with beta derivatives via two integration algorithms. Indian J Phys. 2022;96(7):2093–2105. doi: 10.1007/s12648-021-02168-0
- Zaky MA, Hendy AS, De Staelen RH. Alikhanov Legendre-Galerkin spectral method for the coupled nonlinear time-space fractional Ginzburg-Landau complex system. Mathematics. 2021;9(2):183. doi: 10.3390/math9020183
- Ali KK, Maneea M, Mohamed MS. Solving nonlinear fractional models in superconductivity using the q-Homotopy analysis transform method. J Math. 2023;2023:Article ID 6647375.
- Semary MS, Hassan HN, Radwan AG. Single and dual solutions of fractional order differentia equations based on controlled Picard's method with Simpson rule. J Assoc Arab Univ Basic Appl Sci. 2017;24:247–253.
- Semary MS, Hassan HN, Radwan AG. Controlled Picard method for solving nonlinear fractional reaction-diffusion models in porous catalysts. Chem Eng Commun. 2017;204:635–647. doi: 10.1080/00986445.2017.1300151
- Fareed AF, Elsisy MA, Semary MS, et al. Controlled Picard's transform technique for solving a type of time fractional Navier-Stokes equation resulting from incompressible fluid flow. Int J Appl Comput Math. 2022;8(184):1–15.
- Podlubny I. Fractional differential equations. New York: Academic Press; 1999.
- Abdeljawad T, Baleanu D. On fractional derivatives with exponential kernel and their discrete versions. Rep Math Phys. 2017;80(1):11–27. doi: 10.1016/S0034-4877(17)30059-9
- Veeresha P, Baskonus HM, Gao W. Strong interacting internal waves in rotating ocean: novel fractional approach. Axioms. 2021;10:123. doi: 10.3390/axioms10020123
- Ray SS. Nonlinear differential equations in physics. Berlin, Germany: Springer; 2020.
- Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl. 2015;1(2):73–85.
- Delgado VF, Aguilar JF, Saad K, et al. Application of the Caputo-Fabrizio and Atangana-Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect. Math Methods Appl Sci. 2019;42(4):1167–1193. doi: 10.1002/mma.v42.4
- Naghshband S, Araghi MAF. Solving generalized quintic complex Ginzburg-Landau equation by homotopy analysis method. Ain Shams Eng J. 2018;9(4):607–613. doi: 10.1016/j.asej.2016.01.015