Numerical simulation for fractional Jaulent–Miodek equation associated with energy-dependent Schrödinger potential using two novel techniques

References

• Caputo M. Linear model of dissipation whose Q is almost frequency independent-II. Geophys J Int. 1967;13(5):529–539.
   Web of Science ®Google Scholar
• Ross B. A brief history and exposition of the fundamental theory of fractional calculus. Fractional Calculus and Its Applications, Courant Lect Notes Math,457; 1975. p. 1–36.
   Google Scholar
• Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.
   Google Scholar
• Baleanu D, Guvenc ZB, Tenreiro Machado JA. New trends in nanotechnology and fractional calculus applications. New York: Springer Dordrecht Heidelberg; 2010.
   Google Scholar
• Holm S, Nasholm SP. Comparison of fractional wave equations for power law attenuation in ultrasound and elastography. Ultrasound Med Biol. 2014;40(4):695–703.
   PubMed Web of Science ®Google Scholar
• Metzler R, Klafter J. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep. 2000;339:1–77.
   Web of Science ®Google Scholar
• Atangana A, Bildik N. The use of fractional order derivative to predict the groundwater flow. Math Prob Eng 2013;1:1–9.
   Google Scholar
• Veeresha P, Prakasha DG, Baskonus HM. New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives. Chaos. 2019;29(013119):1–14. doi:https://doi.org/10.1063/1.5074099.
   Google Scholar
• Prakash A, Veeresha P, Prakasha DG, et al. A homotopy technique for fractional order multi-dimensional telegraph equation via Laplace transform. Eur Phys J Plus. 2019;134(19):1–18. doi:https://doi.org/10.1140/epjp/i2019-12411-y.
   Google Scholar
• Veeresha P, Prakasha DG, Baleanu D. An efficient numerical technique for the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equation. Mathematics. 2019;7(3):1–18. doi:https://doi.org/10.3390/math7030265.
   Web of Science ®Google Scholar
• Kumar D, Singh J, Baleanu D, et al. Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel. Phys A. 2018;492:155–167.
   Web of Science ®Google Scholar
• Singh J, Kumar D, Baleanu D. New aspects of fractional Biswas–Milovic model with Mittag-Leffler law. Math Model Nat Phenom. 2019;14:1–23. doi:https://doi.org/10.1051/mmnp/2018068.
   Web of Science ®Google Scholar
• Singh J, Kumar D, Baleanu D. On the analysis of fractional diabetes model with exponential law. Adv Differ Equ. 2018;231; doi:https://doi.org/10.1186/s13662-018-1680-1.
   Google Scholar
• Prakasha DG, Veeresha P, Rawashdeh MS. Numerical solution for (2+1)-dimensional time-fractional coupled Burger equations using fractional natural decomposition method. Math Meth Appl Sci. 2019;42(10):3409–3427. doi:https://doi.org/10.1002/mma.5533.
   Web of Science ®Google Scholar
• Prakasha DG, Veeresha P, Baskonus HM. Two novel computational techniques for fractional Gardner and Cahn-Hilliard equations. Comp and Math Methods. 2019;1(2):1–19. doi:https://doi.org/10.1002/cmm4.1021.
   Google Scholar
• Prakasha DG, Veeresha P, Baskonus HM. Residual power series method for fractional Swift-Hohenberg equation. Fractal Frac. 2019;3(1):1–16. doi:https://doi.org/10.3390/fractalfract3010009.
   Web of Science ®Google Scholar
• Veeresha P, Prakasha DG. Solution for fractional Zakharov–Kuznetsov equations by using two reliable techniques. Chinese J Phys. 2019;60:313–330.
   Web of Science ®Google Scholar
• Liouville J. Memoire sur quelques questions de geometrie et de mecanique, et sur un nouveau genre de calcul pour resoudre ces questions. J Ecole Polytech 1832;13:1–69.
   Google Scholar
• Riemann GFB. Versuch einer allgemeinen Auffassung der Integration und Differentiation. Leipzig: Gesammelte Mathematische Werke; 1896.
   Google Scholar
• Caputo M. Elasticita e Dissipazione. Bologna: Zanichelli; 1969.
   Google Scholar
• Miller KS, Ross B. An introduction to fractional calculus and fractional differential equations. New York: A Wiley; 1993.
   Google Scholar
• Podlubny I. Fractional differential equations. New York: Academic Press; 1999.
   Google Scholar
• Lin W. Global existence theory and chaos control of fractional differential equations. J Math Anal Appl. 2007;332(1):709–726.
   Web of Science ®Google Scholar
• Li Y, Liub F, Turner IW, et al. Time-fractional diffusion equation for signal smoothing. Appl Math Comput. 2018;326:108–116.
   Web of Science ®Google Scholar
• Nasrolahpour H. A note on fractional electrodynamics. Commun Nonlinear Sci Numer Simulat. 2013;18:2589–2593.
   Web of Science ®Google Scholar
• Veeresha P, Prakasha DG, Baskonus HM. Solving smoking epidemic model of fractional order using a modified homotopy analysis transform method. Math Sci. 2019. doi:https://doi.org/10.1007/s40096-019-0284-6.
   Google Scholar
• Prakasha DG, Veeresha P, Baskonus HM. Analysis of the dynamics of hepatitis E virus using the Atangana-Baleanu fractional derivative. Eur Phys J Plus. 2019;134(241):1–11. doi:https://doi.org/10.1140/epjp/i2019-12590-5.
   Google Scholar
• Veeresha P, Prakasha DG, Qurashi MA, et al. A reliable technique for fractional modified Boussinesq and approximate long wave equations. Adv Differ Equ. 2019;253:1–23. doi:https://doi.org/10.1186/s13662-019-2185-2.
   Google Scholar
• Veeresha P, Prakasha DG, Baskonus HM. An efficient technique for a fractional-order system of equations describing the unsteady flow of a polytropic gas. Pramana – J Phys. 2019: 1–12. doi:https://doi.org/10.1007/s12043-019-1829-9.
   Google Scholar
• Veeresha P, Prakasha DG, Baleanu D. An efficient numerical technique for the nonlinear fractional Kolmogorov–petrovskii–piskunov equation. Mathematics. 2019;7(3):1–18. doi:https://doi.org/10.3390/math7030265.
   Web of Science ®Google Scholar
• Jaulent M, Miodek I. Nonlinear evolution equations associated with energy-dependent Schrodinger potentials. Lett Math Phys. 1976;1:243–250.
   Web of Science ®Google Scholar
• Jaulent M. Inverse scattering problems in absorbing media. J Math Phys. 1976;17:1351–1360.
   Web of Science ®Google Scholar
• Das GC, Sarma J, Uberoi C. Explosion of a soliton in a multicomponent plasma. Phys Plasmas. 1997;4(6):2095–2100.
   Web of Science ®Google Scholar
• Atangana A, Baleanu D. Nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations within Sumudu transform. Abstr Appl Anal. 2013: 1–8. Article ID 160681. doi:https://doi.org/10.1155/2013/160681.
   Google Scholar
• Gupta AK, Ray SS. An investigation with Hermite Wavelets for accurate solution of fractional Jaulent–Miodek equation associated with energy-dependent Schrodinger potential. Appl Math Comput. 2015;270:458–471.
   Web of Science ®Google Scholar
• Majlesi A, Ghehsareha HR, Zaghian A. On the fractional Jaulent-Miodek equation associated with energy-dependent Schrodinger potential: Lie symmetry reductions, explicit exact solutions and conservation laws. Eur Phys J Plus. 2017;132:1–13. doi:https://doi.org/10.1140/epjp/i2017-11793-0.
   Web of Science ®Google Scholar
• Yildirim A, Kelleci A. Numerical simulation of the Jaulent–Miodek equation by He’s homotopy perturbation method. World Appl Sci J. 2009;7:84–89.
   Google Scholar
• He JH, Zhang LN. Generalized solitary solution and compacton-like solution of the Jaulent–Miodek equations using the Exp-function method. Phys Lett A. 2008;372(7):1044–1047.
   Web of Science ®Google Scholar
• Rashidi MM, Domairry G, Dinarvand S. The homotopy analysis method for explicit analytical solutions of Jaulent–Miodek equations. Numer Meth Partial Differ Equat. 2009;25(2):430–439.
   Web of Science ®Google Scholar
• Keskin Y, Oturanc G. Reduced differential transform method for partial differential equations. Int J Nonlienar Sci Numer Simul 2009;10(6):741–749.
   Web of Science ®Google Scholar
• Saravanan A, Magesh N. An efficient computational technique for solving the Fokker-Planck equation with space and time fractional derivatives. J King Saud Univ-Sci. 2016;28:160–166.
   Web of Science ®Google Scholar
• Saravanan A, Magesh N. A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell–Whitehead–Segel equation. J Egypt Math Soc 2003;21(3):259–265.
   Google Scholar
• Ray SS. Soliton solutions for time fractional coupled modified KdV equations using new coupled fractional reduced differential transform method. J Math Chem. 2013;51:2214–2229.
   Web of Science ®Google Scholar
• Ray SS. A new coupled fractional reduced differential transform method for the numerical solutions of (2+1)-dimensional time fractional coupled Burger equations. Modell Simulat Eng. 2014: 1–12. doi:https://doi.org/10.1155/2014/960241.
   Google Scholar
• Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems [Ph.D. thesis]. Shanghai Jiao Tong University, 1992.
   Google Scholar
• Liao SJ. Homotopy analysis method: a new analytic method for nonlinear problems. Appl Math Mech. 1998;19:957–962.
   Web of Science ®Google Scholar
• Singh J, Kumar D, Swroop R. Numerical solution of time- and space-fractional coupled Burgers’ equations via homotopy algorithm. Alexandria Eng J. 2016;55(2):1753–1763.
   Web of Science ®Google Scholar
• Kumar D, Singh J, Baleanu D. A new numerical algorithm for fractional Fitzhugh–Nagumo equation arising in transmission of nerve impulses. Nonlinear Dyn. 2018;91:307–317.
   Web of Science ®Google Scholar
• Srivastava HM, Kumar D, Singh J. An efficient analytical technique for fractional model of vibration equation. Appl Math Model. 2017;45:192–204.
   Web of Science ®Google Scholar
• Kumar D, Singh J, Prakash A, et al. Numerical simulation for system of time-fractional linear and nonlinear differential equations. Progr Fract Differ Appl 2019;5(1):65–77.
   Google Scholar
• Prakash A, Veeresha P, Prakasha DG, et al. A new efficient technique for solving fractional coupled Navier–Stokes equations using q-homotopy analysis transform method. Pramana-J Phys 2019;93(6):1–10. doi:https://doi.org/10.1007/s12043-019-1763-x.
   Google Scholar
• Veeresha P, Prakasha DG. A novel technique for (2+1)-dimensional time-fractional Coupled Burgers equations, (2019). doi:https://doi.org/10.1016/j.matcom.2019.06.005.
   Google Scholar
• Veeresha P, Prakasha DG, Baskonus HM. Novel simulations to the time–fractional Fisher’s equation. Math Sci. 2019;13(1):33–42. doi:https://doi.org/10.1007/s40096-019-0276-6.
   Google Scholar
• Prakash A, Prakasha DG, Veeresha P. A reliable algorithm for time-fractional Navier-Stokes equations via Laplace transform. Nonlinear Eng. 2019. doi:https://doi.org/10.1515/nleng-2018-0080.
   Google Scholar
• Veeresha P, Prakasha DG. q-HATM to solve fractional differential equations. Mauritius: Lambert Academic Publishing; 2019.
   Google Scholar
• Fatoorehchi H, Abolghasemi H, Magesh N. The differential transform method as a new computational tool for Laplace transforms. Natl Acad Sci Lett. 2015;38(2):157–160.
   Web of Science ®Google Scholar
• Odibat ZM, Shawagfeh NT. Generalized Taylor’s formula. Appl Math Comput 2007;186(1):286–293.
   Web of Science ®Google Scholar
• Kumar D, Singh J, Baleanu D. A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves. Math Meth Appl Sci. 2017;40:5642–5653.
   Web of Science ®Google Scholar