Abdou, M.A.: An analytical method for space-time fractional nonlinear differential equations arising in plasma physics. J. Ocean Eng. Sci. 2(4), 288–292 (2017)
Goswami, A., Singh, J., Kumar, D., Gupta, S.: An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma. J. Ocean Eng. Sci. 4(2), 85–99 (2019)
Tamboli, V.K., Tandel, P.V.: Solution of the time-fractional generalized Burger–Fisher equation using the fractional reduced differential transform method. J. Ocean Eng. Sci. 6, 66 (2021)
Islam, M.T., Akbar, M.A., Gómez-Aguilar, J.F., Bonyah, E., Fernandez-Anaya, G.: Assorted soliton structures of solutions for fractional nonlinear Schrodinger types evolution equations. J. Ocean Eng. Sci. 6, 66 (2021)
Ionescu, C., Lopes, A., Copot, D., Machado, J.A.T., Bates, J.H.T.: The role of fractional calculus in modeling biological phenomena: a review. Commun. Nonlinear Sci. Numer. Simul. 51, 141–159 (2017)
Zubair, T., Usman, M., Ali, U., Mohyud-Din, S.T.: Homotopy analysis method for system of partial differential equations. Int. J. Mod. Eng. Sci. 1(2), 67–79 (2012)
Elsaid, A.: Homotopy analysis method for solving a class of fractional partial differential equations. Commun. Nonlinear Sci. Numer. Simul. 16(9), 3655–3664 (2011)
Abbasbandy, S.: The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation. Phys. Lett. A 361(6), 478–483 (2007)
Bataineh, A.S., Noorani, M.S.M., Hashim, I.: Approximate analytical solutions of systems of PDEs by homotopy analysis method. Comput. Math. Appl. 55(12), 2913–2923 (2008)
Vahidi, J.: The combined Laplace-homotopy analysis method for partial differential equations. J. Math. Comput. Sci. 16, 88–102 (2016)
Morales-Delgado, V.F., Gómez-Aguilar, J.F., Yépez-Martínez, H., Baleanu, D., Eskobar-Jimenez, R.F., Olivares-Peregrino, V.H.: Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular. Adv. Differ. Equ. 2016(1), 1–17 (2016)
El-Sayed, A.M., Elsaid, A., El-Kalla, I.L., Hammad, D.: A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains. Appl. Math. Comput. 218(17), 8329–8340 (2012)
Momani, S., Odibat, Z.: Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys. Lett. A 365(5–6), 345–350 (2007)
Wang, Q.: Homotopy perturbation method for fractional KdV-Burgers equation. Chaos Solitons Fract. 35(5), 843–850 (2008)
Jafari, H., Nazari, M., Baleanu, D., Khalique, C.M.: A new approach for solving a system of fractional partial differential equations. Comput. Math. Appl. 66(5), 838–843 (2013)
Odibat, Z., Momani, S.: Numerical methods for nonlinear partial differential equations of fractional order. Appl. Math. Model. 32(1), 28–39 (2008)
Odibat, Z., Momani, S.: Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Numer. Simul. 7(1), 27–34 (2006)
Inc, M.: The approximate and exact solutions of the space and time-fractional Burgers equations with initial conditions by variational iteration method. J. Math. Anal. Appl. 345(1), 476–484 (2008)
Abassy, T.A., El-Tawil, M.A., El-Zoheiry, H.: Modified variational iteration method for Boussinesq equation. Comput. Math. Appl. 54(7–8), 955–965 (2007)
Haq, I.U., Ullah, Z.: Natural decomposition method and coupled systems of nonlinear fractional order partial differential equations. Results Nonlinear Anal. 3(1), 35–44 (2020)
Rawashdeh, M.S., Maitama, S.: Solving coupled system of nonlinear PDE’s using the natural decomposition method. Int. J. Pure Appl. Math. 92(5), 757–776 (2014)
Momani, S., Arqub, O.A., Maayah, B.: Piecewise optimal fractional reproducing kernel solution and convergence analysis for the Atangana–Baleanu–Caputo model of the Lienard’s equation. Fractals (2020). https://doi.org/10.1142/S0218348X20400071
Maayah, B., Yousef, F., Arqub, O.A., Momani, S., Alsaedi, A.: Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in Hilbert space with error analysis. Filomat 33(12), 3845–3853 (2019)
Arqub, O.A., Hayat, T., Alhodaly, M.: Reproducing kernel Hilbert pointwise numerical solvability of fractional Sine–Gordon model in time-dependent variable with Dirichlet condition. Phys. Scr. (2021). https://doi.org/10.1088/1402-4896/ac0c58
Arqub, O.A.: Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions. Comput. Math. Appl. 73(6), 1243–1261 (2017)
Arqub, O.A., Shawagfeh, N.: Application of reproducing kernel algorithm for solving Dirichlet time-fractional diffusion-Gordon types equations in porous media. J. Porous Media 22(4), 66 (2019)
Al-Smadi, M., Arqub, O.A., Gaith, M.: Numerical simulation of telegraph and Cattaneo fractional-type models using adaptive reproducing kernel framework. Math. Methods Appl. Sci. 44(10), 8472–8489 (2021)
Arqub, O.A.: The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations. Math. Methods Appl. Sci. 39(15), 4549–4562 (2016)
Adomian, G.: A review of the decomposition method and some recent results for nonlinear equations. Comput. Math. Appl. 21(5), 101–127 (1991)
Adomian, G.: A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135(2), 501–544 (1988)
Wang, Q.: Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method. Appl. Math. Comput. 182(2), 1048–1055 (2006)
Khan, H., Shah, R., Kumam, P., Baleanu, D., Arif, M.: Laplace decomposition for solving nonlinear system of fractional order partial differential equations. Adv. Differ. Equ. 2020(1), 1–18 (2020)
Shah, R., Khan, H., Arif, M., Kumam, P.: Application of Laplace–Adomian decomposition method for the analytical solution of third-order dispersive fractional partial differential equations. Entropy 21(4), 335 (2019)
Jafari, H., Khalique, C.M., Nazari, M.: Application of the Laplace decomposition method for solving linear and nonlinear fractional diffussion-wave equations. Appl. Math. Lett. 24(11), 1799–1805 (2011)
Mahmood, S., Shah, R., Khan, H., Arif, M.: Laplace Adomian decomposition method for multi dimensional time fractional model of Navier–Stokes equation. Symmetry 11(2), 149 (2019)
Mohammed, O.H., Salim, H.A.: Computational methods based Laplace decomposition for solving nonlinear system of fractional order differential equations. Alex. Eng. J. 57(4), 3549–3557 (2018)
Mohamed, M.Z., Elzaki, T.M.: Comparison between the Laplace decomposition method and Adomian decomposition in time-space fractional nonlinear fractional differential equations. Appl. Math. 9(04), 448–458 (2019)
Odibat, Z.: An optimized decomposition method for nonlinear ordinary and partial differentail equations. Phys. A Stat. Mech. Appl. 541, 66 (2020). https://doi.org/10.1016/j.physa.2019.123323
Odibat, Z.: The optimized decomposition method for a reliable treatment of IVPs for second order differential equations. Phys. Scr. 6, 66 (2021)
Shah, R., Khan, H., Kumam, P., Arif, M.: An analytical technique to solve the system of nonlinear fractional partial differential equations. Mathematics 7(6), 505 (2019)
Veeresha, P., Prakasha, D.G., Qurashi, M.A., Baleanu, D.: A reliable technique for fractional modified Boussinesq and approximate long wave equations. Adv. Differ. Equ. 2019(1), 1–23 (2019)
Wang, L., Chen, X.: Approximate analytial solutions of time fractional Whitham–Broer–Kaup equations by a residual power series method. Entropy 17(9), 6519–6533 (2015)