Citation: Ebrahem A. Algehyne, Essam R. El-Zahar, Fahad M. Alharbi, Abdelhalim Ebaid. Development of analytical solution for a generalized Ambartsumian equation[J]. AIMS Mathematics, 2020, 5(1): 249-258. doi: 10.3934/math.2020016
[1] | V. A. Ambartsumian, On the fluctuation of the brightness of the milky way, Doklady Akad. Nauk USSR, 44 (1944), 223-226. |
[2] | J. Patade, S. Bhalekar, On analytical solution of Ambartsumian equation, Natl. Acad. Sci. Lett., 40 (2017), 291-293. doi: 10.1007/s40009-017-0565-2 |
[3] | T. Kato, J. B. McLeod, The functional-differential equation y'(x) = ay(λx)+by(x), Bull. Am. Math. Soc., 77 (1971), 891-935. |
[4] | H. O. Bakodah, A. Ebaid, Exact solution of Ambartsumian delay differential equation and comparison with Daftardar-Gejji and Jafari approximate method, Mathematics, 6 (2018), 331. |
[5] | D. Kumar, J. Singh, D. Baleanu, et al. Analysis of a fractional model of the Ambartsumian equation, Eur. Phys. J. Plus, 133 (2018), 133-259. doi: 10.1140/epjp/i2018-11954-7 |
[6] | Q. Feng, A new approach for seeking coefficient function solutions of conformable fractional partial differential equations based on the Jacobi elliptic equation, Chin. J. Phys., 56 (2018), 2817-2828. doi: 10.1016/j.cjph.2018.08.006 |
[7] | A. Ebaid, B. Masaedeh, E. El-Zahar, A new fractional model for the falling body problem, Chin. Phys. Lett., 34 (2017), 020201. |
[8] | H. C. Yaslan, Numerical solution of the conformable space-time fractional wave equation, Chin. J. Phys., 56 (2018), 2916-2925. doi: 10.1016/j.cjph.2018.09.026 |
[9] | H. Rezazadeh, H. Tariq, M. Eslami, et al. New exact solutions of nonlinear conformable timefractional Phi-4 equation, Chin. J. Phys., 56 (2018), 2805-2816. doi: 10.1016/j.cjph.2018.08.001 |
[10] | G. Adomian, R. Rach, Algebraic equations with exponential terms, J. Math. Anal. Appl., 112 (1985), 136-140. doi: 10.1016/0022-247X(85)90280-X |
[11] | G. Adomian, R. Rach, Algebraic computation and the decomposition method, Kybernetes, 15 (1986), 33-37. doi: 10.1108/eb005727 |
[12] | A. M. Wazwaz, Adomian decomposition method for a reliable treatment of the Bratu-type equations, Appl. Math. Comput., 166 (2005), 652-663. |
[13] | A. M. Wazwaz, The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations, Appl. Math. Comput., 216 (2010), 1304-1309. |
[14] | A. Ebaid, Approximate analytical solution of a nonlinear boundary value problem and its application in fluid mechanics, Z. Naturforschung A., 66 (2011), 423-426. |
[15] | A. Ebaid, A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method, J. Comput. Appl. Math., 235 (2011), 1914-1924. doi: 10.1016/j.cam.2010.09.007 |
[16] | E. H. Ali, A. Ebaid, R. Rach, Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions, Comput. Math. Appl., 63 (2012), 1056-1065. doi: 10.1016/j.camwa.2011.12.010 |
[17] | C. Chun, A. Ebaid, M. Lee, et al. An approach for solving singular two point boundary value problems: Analytical and numerical treatment, ANZIAM J., 53 (2012), 21-43. |
[18] | A. M. Wazwaz, R. Rach, J. S. Duan, Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions, Appl. Math. Comput., 219 (2013), 5004-5019. |
[19] | H. Triki, Solitons and periodic solutions to the dissipation-modified KdV equation with timedependent coefficients, Rom. J. Phys., 59 (2014), 421-432. |
[20] | A. Ebaid, M. D. Aljoufi, A. M. Wazwaz, An advanced study on the solution of nanofluid flow problems via Adomian's method, Appl. Math. Lett., 46 (2015), 117-122. doi: 10.1016/j.aml.2015.02.017 |
[21] | A. Alshaery, A. Ebaid, Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method, Acta Astronaut., 140 (2017), 27-33. doi: 10.1016/j.actaastro.2017.07.034 |
[22] | A. M. Wazwaz, M. A. Z. Raja, M. I. Syam, Reliable treatment for solving boundary value problems of pantograph delay differential equation, Rom. Rep. Phys., 69 (2017), 69-102. |
[23] | A. A. Gaber, A. Ebaid, Analytical study on the slip flow and heat transfer of nanofluids over a stretching sheet using Adomian's method, Rom. Rep. Phys., 70 (2018), 1-15. |
[24] | A. K. Golmankhaneh, A. K. Golmankhaneh, D. Baleanu, Homotopy perturbation method for solving a system of Schrodinger-Korteweg-De Vries equations, Rom. Rep. Phys., 63 (2011), 609-623. |
[25] | A. Patra, S. S. Ray, Homotopy perturbation sumudu transform method for solving convective radial fins with temperature-dependent thermal conductivity of fractional order energy balance equation, Int. J. Heat Mass Tran., 76 (2014), 162-170. doi: 10.1016/j.ijheatmasstransfer.2014.04.020 |
[26] | Z. Ayati, J. Biazar, On the convergence of Homotopy perturbation method, J. Egypt. Math. Soc., 23 (2015), 424-428. doi: 10.1016/j.joems.2014.06.015 |
[27] | S. M. Khaled, E. R. El-Zahar, A. Ebaid, Solution of Ambartsumian delay differential equation with conformable eerivative, Mathematics, 7 (2019), 425. |
[28] | M. Turkyilmazoglu, Accelerating the convergence of decomposition method of Adomian, J. Comput. Sci., 31 (2019), 54-59. doi: 10.1016/j.jocs.2018.12.014 |
[29] | M. Turkyilmazoglu, Convergence accelerating in the homotopy analysis method: A new approach, Adv. Appl. Math. Mech., 10 (2018), 925-947. doi: 10.4208/aamm.OA-2017-0196 |
[30] | M. Turkyilmazoglu, Is homotopy perturbation method the traditional Taylor series expansion, Hacet. J. Math. Stat., 44 (2015), 651-657. |