Natural homotopy perturbation method for solving nonlinear fractional gas dynamics equations

[1] W. H. Su, D. Baleanu, X.J. Yang, and H. Jafari, Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method, Fixed Point Theo. Appl. 2013 (2013) 1–11.

[2] H. Jafari and H.K. Jassim, Local fractional variational iteration method for nonlinear partial differential equations within local fractional operators, Appl. Appl. Math. 10 (2015) 1055–1065.

[3] X.J. Yang, Local Fractional Functional Analysis and its Applications, Asian Academic, Hong Kong, China, 2011.

[4] S. Xu, X. Ling, Y. Zhao, and H.K. Jassim, A novel schedule for solving the two-dimensional diffusion in fractal heat transfer, Therm. Sci. 19 (2015) S99–S103.

[5] X. Yang, Advanced Local Fractional Calculus and its Applications, World Science Publisher, New York, 2012.

[6] H. K. Jassim, J. Vahidiand and V.M. Ariyan, Solving Laplace equation within local fractional operators by using local fractional differential transform and Laplace variational iteration methods, Nonlinear Dyn. Syst. Theo. 20(4) (2020) 388–396.

[7] X.J. Yang, J.A. Machad and H.M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach, Appl. Math. Comput. 274 (2016) 143–151.

[8] A.M. Yang,  X.J. Yang, and Z.B. Li, Local fractional series expansion method for solving wave and diffusion equations Cantor sets, Abstr. Appl. Anal. 2013 (2013) 1–5.

[9] H.K. Jassim and D. Baleanu, A novel approach for Korteweg-de Vries equation of fractional order, J. Appl. Comput. Mech. 5(2) (2019) 192–198.

[10] H.M. Srivastava, A.K. Golmankhaneh and D. Baleanu, Local fractional Sumudu transform with application to IVPs on Cantor set, Abstr. Appl. Anal. 2014 (2014) 1–7.

[11] C.G. Zhao, A.M. Yang, H. Jafari, and A. Haghbin, The Yang-Laplace transform for solving the IVPs with local fractional derivative, Abstr. Appl. Anal. 2014 (2014) 1–5.

[12] H.K. Jassim, The analytical solutions for Volterra integro-differential equations involving local fractional operators by Yang-Laplace transform, Sahand Commun. Math. Anal. 6(1) (2017) 69-76.

[13] Y. Zhang, X.J. Yang, and C. Cattani, Local fractional homotopy perturbation method for solving nonhomogeneous heat conduction equations in fractal domains, Entropy 17 (2015) 6753–6764.

[14] H.K. Jassim, New approaches for solving Fokker Planck equation on Cantor sets within local fractional operators, J. Math. 2015 (2015) 1–8

[15] H.K. Jassim, Local fractional Laplace decomposition method for nonhomogeneous heat equations arising in fractal heat flow with local fractional derivative, Int. J. Adv. Appl. Math. Mech. 2 (2015) 1–7.

[16] M.S. Hu, R.P. Agarwal, and X.J. Yang, Local fractional Fourier series with application to wave equation in fractal vibrating, Abstr. Appl. Anal. 2012 (2012) 1–7.

[17] H.K. Jassim, C. Unlu, S.P. Moshokoa and C.M. Khalique, Local fractional Laplace variational iteration method for solving diffusion and wave equations on Cantor sets within local fractional operators, Math. Prob. Engin. 2015 (2015) 1–7.

[18] H. Jafari and H.K. Jassim, A Coupling method of local fractional variational iteration method and Yang-Laplace transform for solving Laplace equation on Cantor sets, Int. J. Pure Appl. Sci. Tech. 26 (2015) 24–33.

[19] C.F. Liu, S.S. Kong, and J. Zhao, Local fractional Laplace variational iteration method for fractal vehicular traffic flow, Adv. Math. Phys. 2014 (2014) 1–7.

[20] Y. Li, L.F. Wang, and S.J. Yuan, Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem, Therm. Sci. 17 (2013) 715–721.

[21] D. Baleanu and H.K. Jassim, Exact solution of two-dimensional fractional partial differential equations, Fractal Fractional 4 (21) (2020) 1–9.

[22] H.K. Jassim, M.G. Mohammed and H.A. Eaued, A modification fractional homotopy analysis method for solving partial differential equations arising in mathematical physics, IOP Conf. Ser.: Mater. Sci. Engin. 928 (042021) (2020) 1–22.

[23] H.A. Eaued, H.K. Jassim and M.G. Mohammed, A Novel method for the analytical solution of partial differential equations arising in mathematical physics, IOP Conf. Ser.: Mater. Sci. Engin.  928 (042037) (2020) 1-16.

[24] H.K. Jassim and J. Vahidi, A new technique of reduce differential transform method to solve local fractional PDEs in mathematical physics, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 37–44.

[25] S.M. Kadhim, M.G. Mohammad and H.K. Jassim, How to obtain Lie point symmetries of PDEs, J. Math. Comp. Sci. 22 (2021) 306–324.

[26] H.K. Jassim and M.A. Shareef, On approximate solutions for fractional system of differential equations with Caputo-Fabrizio fractional operator, J. Math. Comp. Sci. 23 (2021) 58–66.

[27] H.K. Jassim, S.A. Khafif, SVIM for solving Burger’s and coupled Burger’s equations of fractional order, Prog. Frac. Diff. Appl. 7(1) (2021) 1–6.

[28] H.K. Jassim and H.A. Kadhim, Fractional Sumudu decomposition method for solving PDEs of fractional order, J. Appl. Comput. Mech. 7(1) (2021) 302–311.

[29] H. Jafari, H.K. Jassim, D. Baleanu and Y.M. Chu, On the approximate solutions for a system of coupled Korteweg-de Vries equations with local fractional derivative, Fractals 29(5) (2021) 1–7.

[30] H. Jafari, H.K. Jassim, S.P. Moshokoa, V.M. Ariyan and F. Tchier, Reduced differential transform method for partial differential equations within local fractional derivative operators, Adv. Mech. Engin. 8 (2016)1–6.

[31] D. Baleanu, H.K. Jassim and H. Khan, A modification fractional variational iteration method for solving nonlinear gas dynamic and coupled KdV equations involving local fractional operators, Ther. Sci. 22 (2018) S165–S175.

[32] S. Kumar and M.M. Rashidi, New analytical method for gas dynamics equation arising in shock fronts, Comp. Phy. Commun. 185(7) (2014) 1947–1954.

[33] H. Jafari and H.K. Jassim, Local fractional Laplace variational iteration method for solving nonlinear partial differential equations on Cantor sets within local fractional operators, J. Zankoy Sulaimani-Part A 16 (4) (2014) 49–57.

[34] S. Das and R. Kumar, Approximate analytical solution of fractional gas dynamic equations, Appl. Math. Comput. 217(24) (2011), 9905–9915.