Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes

References

• Yue C, Khater MM, Attia RA, et al. The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–baleanu derivative operator. Adv Differ Equ. 2020;2020(1):1–12.
   Web of Science ®Google Scholar
• Baleanu D, Fernandez A, Akgül A. On a fractional operator combining proportional and classical differintegrals. Mathematics. 2020;8(3):360.
   Web of Science ®Google Scholar
• Khater MM, Park C, Lu D, et al. Analytical, semi-analytical, and numerical solutions for the Cahn–allen equation. Adv Differ Equ. 2020;2020(1):1–12.
   Web of Science ®Google Scholar
• Akgül A. A novel method for a fractional derivative with non-local and non-singular kernel. Chaos. Solitons & Fractals. 2018;114:478–482.
   Web of Science ®Google Scholar
• Akgül EK. Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives. Chaos: An Interdisciplinary J Nonlinear Sci. 2019;29(2):023108.
   PubMed Web of Science ®Google Scholar
• Houwe A, Inc M, Doka SY, et al. Chirped solitons in negative index materials generated by Kerr nonlinearity. Results Phys. 2020;17. doi:10.1016/j.rinp.2020.103097.
   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 (Stuttg). 2020;206; doi:10.1016/j.ijleo.2019.163332.
   Web of Science ®Google Scholar
• Yépez-Martínez H, Gómez-Aguilar JF. Fractional sub-equation method for Hirota–satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative. Waves Random Complex Media. 2019;29(4):678–693.
   Web of Science ®Google Scholar
• Aslan EC, Inc M. Optical soliton solutions of the NLSE with quadratic-cubic-Hamiltonian perturbations and modulation instability analysis. Optik (Stuttg). 2019;196:162661.
   Web of Science ®Google Scholar
• Pinar Z. On the explicit solutions of fractional Bagley-Torvik equation arises in engineering. An Int J Optimization Control: Theories & Applications (IJOCTA). 2019;9(3):52–58.
   Google Scholar
• Abdel-Aty AH, Khater M, Attia RA, et al. Exact traveling and nano-solitons wave solitons of the ionic waves propagating along microtubules in living cells. Mathematics. 2020;8(5):697.
   Web of Science ®Google Scholar
• Morales-Delgado VF, Gómez-Aguilar JF, Taneco-Hernandez MA. Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense. AEU-Int J Electron Commun. 2018;85:108–117.
   Web of Science ®Google Scholar
• Li J, Attia RA, Khater MM, et al. The new structure of analytical and semi-analytical solutions of the longitudinal plasma wave equation in a magneto-electro-elastic circular rod. Mod Phys Lett B. 2020;34(12). doi:10.1142/S0217984920501237
   Web of Science ®Google Scholar
• Jajarmi A, Yusuf A, Baleanu D, et al. A new fractional hrsv model and its optimal control: a non-singular operator approach. Physica A. 2020;547; doi:10.1016/j.physa.2019.123860.
   Web of Science ®Google Scholar
• Yue C, Khater MM, Inc M, et al. Abundant analytical solutions of the fractional nonlinear (2 + 1)-dimensional BLMP equation arising in incompressible fluid. Int J Mod Phys B. 2020. doi:10.1142/S0217979220500848.
   Web of Science ®Google Scholar
• Houwe A, Abbagari S, Salathiel Y, et al. Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations. Results in Physics. 2020. doi:10.1016/j.rinp.2020.103127.
   Google Scholar
• Khater MM, Attia RA, Alodhaibi SS, et al. Novel soliton waves of two fluid nonlinear evolutions models in the view of computational scheme. Int J Mod Phys B. 2020. doi:10.1142/S0217979220500964.
   Web of Science ®Google Scholar
• Yépez-Martínez H, Gómez-Aguilar JF, Atangana A. First integral method for non-linear differential equations with conformable derivative. Math Model Nat Phenom. 2018;13(1):14.
   Web of Science ®Google Scholar
• Yue C, Khater MM, Attia RA, et al. Computational simulations of the couple Boiti–leon–pempinelli (BLP) system and the (3 + 1)-dimensional Kadomtsev–petviashvili (KP) equation. AIP Adv. 2020;10(4):045216.
   Web of Science ®Google Scholar
• Yépez-Martínez H, Gómez-Aguilar JF. M-derivative applied to the dispersive optical solitons for the Schrödinger-Hirota equation. The European Physical Journal Plus. 2019;134(3):93.
   Web of Science ®Google Scholar
• Yepez-Martinez H, Gomez-Aguilar JF. M-derivative applied to the soliton solutions for the Lakshmanan–porsezian–daniel equation with dual-dispersion for optical fibers. Opt Quantum Electron. 2019;51(1):31.
   Web of Science ®Google Scholar
• Khater MM, Attia RA, Lu D. Computational and numerical simulations for the nonlinear fractional Kolmogorov–petrovskii–piskunov (FKPP) equation. Phys Scr. 2020;95(5):055213.
   Web of Science ®Google Scholar
• Lavalle G, Grenier N, Mergui S, et al. Solitary waves on superconfined falling liquid films. Phys Rev Fluids. 2020;5(3). doi:10.1103/PhysRevFluids.5.032001
   Web of Science ®Google Scholar
• la Forgia G, Tokyay T, Adduce C, et al. Bed shear stress and sediment entrainment potential for breaking of internal solitary waves. Adv Water Resour. 2020;135. doi:10.1016/j.advwatres.2019.103475.
   Web of Science ®Google Scholar
• Khater MM, Attia RA, Abdel-Aty AH, et al. Analytical and semi-analytical ample solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term. Results Phys. 2020;16; doi:10.1016/j.rinp.2020.103000.
   Web of Science ®Google Scholar
• El-Ganaini S, Zayed EM. Short comment on “the extended simplest equation method and the (G′/G,1/G)-expansion method”. Optik (Stuttg). 2020;206; doi:10.1016/j.ijleo.2020.164258.
   Web of Science ®Google Scholar
• Arqub OA, Al-Smadi M. Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions. Soft comput. 2020; 24: 12501–12522.
   Web of Science ®Google Scholar
• Hyder AA, Barakat MA. General improved Kudryashov method for exact solutions of nonlinear evolution equations in mathematical physics. Phys Scr. 2020;95(4):045212.
   Web of Science ®Google Scholar
• Ali A, Seadawy AR, Baleanu D. Propagation of harmonic waves in a cylindrical rod via generalized Pochhammer-Chree dynamical wave equation. Results Phys. 2020. doi:10.1016/j.rinp.2020.103039
   Web of Science ®Google Scholar
• Ganji DD, Abdollahzadeh M. Exact travelling solutions for the Lax’s seventh-order KdV equation by sech method and rational exp-function method. Appl Math Comput. 2008;206(1):438–444.
   Web of Science ®Google Scholar
• Biswas A, Konar S, Zerrad E. Soliton Perturbation Theory for the general modified Degasperis-Procesi Camassa-Holm equation. Int. J. Mod. Math. 2007;2:35–40.
   Google Scholar
• Abbasbandy S. Solitary wave solutions to the modified form of Camassa–holm equation by means of the homotopy analysis method. Chaos. Solitons & Fractals. 2009;39(1):428–435.
   Web of Science ®Google Scholar
• Linares F, Ponce G, Sideris TC. Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons. In Asymptotic analysis for nonlinear dispersive and wave equations. Cornell University; 2016. arXiv:1609.06212v3.
   Google Scholar
• Gao Q, Zhang S, Zhang J. Adaptive moving knots meshless method for Degasperis-Procesi equation with conservation laws. Appl Numer Math. 2019;142:90–101.
   Web of Science ®Google Scholar
• Kadkhoda N, Jafari H. Analytical solutions of the Gerdjikov–ivanov equation by using exp (− φ (ξ))-expansion method. Optik (Stuttg). 2017;139:72–76.
   Web of Science ®Google Scholar
• Khater MM. Exact traveling wave solutions for the generalized Hirota-Satsuma couple KdV system using the exp (φ (ξ))-expansion method. Cogent Math. 2016;3(1). doi:10.1080/23311835.2016.1172397.
   Google Scholar
• Khater MM, Lu D, Attia RA. Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method. AIP Adv. 2019;9(2):025003.
   Web of Science ®Google Scholar
• Khater MM, Attia RA, Abdel-Aty AH, et al. Analytical and semi-analytical ample solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term. Results in Physics. 2020;16. doi:10.1016/j.rinp.2020.103000.
   Web of Science ®Google Scholar
• Ali AT, Khater MM, Attia RA, et al. Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system. Chaos Solitons Fractals. 2020;131. doi:10.1016/j.chaos.2019.109473.
   Web of Science ®Google Scholar
• Attia RA, Lu D, Ak T, et al. Optical wave solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term via modified Khater method. Mod Phys Lett B. 2020;34(05):20500.
   Google Scholar