Citation: Amit Prakash, Manish Goyal, Haci Mehmet Baskonus, Shivangi Gupta. A reliable hybrid numerical method for a time dependent vibration model of arbitrary order[J]. AIMS Mathematics, 2020, 5(2): 979-1000. doi: 10.3934/math.2020068
[1] | H. M. Srivastava, D. Kumar, J. Singh, An efficient analytical technique for fractional model of vibration equation, Appl. Math. Model., 45 (2017), 192-204. doi: 10.1016/j.apm.2016.12.008 |
[2] | H. Singh, Approximate solution of fractional vibration equation using Jacobi polynomials, Appl. Math. Comput., 317 (2018), 85-100. |
[3] | H. Singh, H. M. Srivastava, D. Kumar, A reliable numerical algorithm for the fractional vibration equation, Chaos Soliton. Fract., 103 (2017), 131-138. doi: 10.1016/j.chaos.2017.05.042 |
[4] | S. Das, A numerical solution of the vibration equation using modified decomposition method, J. Sound Vib., 320 (2009), 576-583. doi: 10.1016/j.jsv.2008.08.029 |
[5] | S. Das, P. K. Gupta, Application of homotopy perturbation method and homotopy analysis method for fractional vibration equation, Int. J. Comput. Math., 88 (2011), 430-441. doi: 10.1080/00207160903474214 |
[6] | S. T. Mohyud-Din, A. Yildirim, An algorithm for solving the fractional vibration equation, Comput. Math. Model., 23 (2012), 228-237. |
[7] | H. M. Baskonus, T. Mekkaoui, Z. Hammouch, et al. Active control of a chaotic fractional order economic system, Entropy, 17 (2015), 5771-5783. doi: 10.3390/e17085771 |
[8] | H. M. Baskonus, H. Bulut, On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method, Open Math., 13 (2015), 547-556. |
[9] | H. M. Baskonus, G. Yel, H. Bulut, Novel wave surfaces to the fractional Zakharov- Kuznetsov Benjamin-Bona-Mahony equation, AIP Conference Proceedings, 1863 (2017), 560084. |
[10] | C. Ravichandran, K. Jothimani, H. M. Baskonus, et al. New results on nondensely characterized integrodifferential equations with fractional order, Eur. Phys. J. Plus, 133 (2018), 109. |
[11] | R. Panda, M. Dash, Fractional generalized splines and signal processing, Signal Process, 86 (2006), 2340-2350. doi: 10.1016/j.sigpro.2005.10.017 |
[12] | R. L. Bagley, P. J. Torvik, A theoretical basis for the application of fractional calculus to Viscoelasticity, J. Rheol., 27(1983), 201-210. doi: 10.1122/1.549724 |
[13] | A. Prakash, M. Goyal, S. Gupta, q-homotopy analysis method for fractional Bloch model arising in nuclear magnetic resonance via the Laplace transform, Ind. J. Phys., (2019), http://doi.org/10.1007/s12648-019-01487-7. |
[14] | A. Prakash, M. Goyal, S. Gupta, Numerical simulation of space-fractional Helmholtz equation arising in Seismic wave propagation, imaging and inversion, Pramana, 93 (2019), 28. |
[15] | M. Goyal, H. M. Baskonus, A. Prakash, An efficient technique for a time fractional model of lassa hemorrhagic fever spreading in pregnant women, Eur. Phys. J. Plus, 134 (2019), 482. |
[16] | S. Das, Solution of fractional vibration equation by the variational iteration method and modified decomposition method, Int. J. Nonlin. Sci. Num., 9 (2008), 361-366. |
[17] | S. J. Liao, On the homotopy analysis method for non-linear problems, Appl. Math. Comput., 147 (2004), 499-513. |
[18] | M. A. El-Tawil, S. N. Huseen, The q-homotopy analysis method (q-HAM), Int. J. Appl. Math. Mech., 8 (2012), 51-75. |
[19] | M. A. El-Tawil, S. N. Huseen, On convergence of the q-homotopy analysis method, Int. J. Contemp. Math. Sci., 8 (2013), 481-497. doi: 10.12988/ijcms.2013.13048 |
[20] | A. Prakash, P. Veeresha, D. G. Prakasha, et al. A homotopy technique for a fractional order multi-dimensional telegraph equation via the Laplace Transform, Eur. Phys. J. Plus, 134 (2019), 19. |
[21] | A. Prakash, P. Veeresha, D. G. Prakasha, et al. A new efficient technique for solving fractional coupled Navier-Stokes equations using q-homotopy analysis transform method, Pramana, 93 (2019), 6. |
[22] | A. Prakash, M. Goyal, S. Gupta, Fractional variational iteration method for solving time-fractional Newell-Whitehead-Segel equation, Nonlinear Eng., 8 (2019), 164-171. doi: 10.1515/nleng-2018-0001 |
[23] | M. Goyal, A. Prakash, S. Gupta, Numerical simulation for time-fractional nonlinear coupled dynamical model of romantic and interpersonal relationships, Pramana, 92 (2019), 82. |
[24] | A. Prakash, M. Goyal, S. Gupta, A reliable algorithm for fractional Bloch model arising in magnetic resonance imaging, Pramana, 92 (2019), 18. |
[25] | A. M. S. Mahdy, A. S. Mohamed, A. A. H. Mtawa, Implementation of the Homotopy perturbation Sumudu transform method for solving Klein-Gordon equation, Appl. Math., 6 (2015), 617-628. doi: 10.4236/am.2015.63056 |
[26] | A. A. Elbeleze, A. Kilicman, B. M. Taib, Homotopy perturbation method for fractional Black-Scholes European option pricing equations using Sumudu transform, Math. Probl. Eng., 2013 (2013), 524852. |
[27] | G. K. Watugala, Sumudu transform: A new integral transform to solve differential equations and control engineering problems, Integr. Educ., 24 (1993), 35-43. |
[28] | G. K. Watugala, The Sumudu transform for functions of two variables, Math. Eng. Ind., 8 (2002), 293-302. |
[29] | M. A. Asiru, Further properties of the Sumudu transform and its applications, Int. J. Math. Educ. Sci. Tech., 33 (2002), 441-449. doi: 10.1080/002073902760047940 |
[30] | S. Weerakoon, Applications of Sumudu transform to partial differential equations, Int. J. Math. Educ. Sci. Tech., 25 (1994), 277-283. doi: 10.1080/0020739940250214 |
[31] | S. Weerakoon, Complex inversion formula for Sumudu transforms, Int. J. Math. Educ. Sci. Tech., 29 (1998), 618-621. |
[32] | J. Singh, D. Kumar, D. Baleanu, et al. An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation, Appl. Math. Comput., 335 (2018), 12-24. |
[33] | I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. |
[34] | M. Caputo, Elasticita e Dissipazione, Zani-Chelli, 1969. |
[35] | K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag, 2004. |
[36] | A. Prakash, M. Kumar, D. Baleanu, A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform, Appl. Math. Comput., 334 (2004), 30-40. |
[37] | J. Choi, D. Kumar, J. Singh, et al. Analytical techniques for system of time fractional nonlinear differential equations, J. Korean Math. Soc., 54 (2017), 1209-1229. |