Analytical solution of non-linear fractional order Swift-Hohenberg equations

Kilbas, 1993 Miller, 1993 Podlubny, 1999 Lakshmikantham, 2009 Ahmadian, 2015, Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose, J Comput Phys, 294, 562, 10.1016/j.jcp.2015.03.011 Kilbas, 2006 Ahmadian, 2017, Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution, Commun Nonlinear Sci Numer Simul, 53, 44, 10.1016/j.cnsns.2017.03.012 Ahmadian, 2015, Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose, J Comput Phys, 294, 562, 10.1016/j.jcp.2015.03.011 Sarwar, 2016, Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method, Waves Random Complex Media, 26, 365, 10.1080/17455030.2016.1158436 Abelman, 2017, Subordination conditions for a class of non-Bazilevic type defined by using fractional q–calculus operators. Facta universitatis (NIS) Math, Inform, 32, 255 Klapp, 2014 Diaz, 1985 Arnold, 1949 William, 1965 Prakasha, 2019, Residual power series method for fractional Swift-Hohenberg equation, Fractal Fract, 3, 9, 10.3390/fractalfract3010009 Swift, 1977, Hydrodynamics fluctuations at the convective instability, Phys Rev A, 15, 319, 10.1103/PhysRevA.15.319 Ryabov, 2017, Nonlinear waves described by the generalized Swift-Hohenberg equation, J Phys Conf Ser, 788, 012032, 10.1088/1742-6596/788/1/012032 Ahmadian, 2017, Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution, Commun Nonlinear Sci Numer Simul, 53, 44, 10.1016/j.cnsns.2017.03.012 Fife PC. Pattern formation in gradient systems, In handbook of dynamical systems, Elsevier: Amsterdam, Netherlands, 2002;2:679–719. Hoyle, 2006 Ryabov, 2017, Nonlinear waves described by the generalized Swift-Hohenberg equation, J Phys Conf Ser, 788, 012032, 10.1088/1742-6596/788/1/012032 Lega, 1994, Swift-Hohenberg equation for lasers, Phys Rev Lett, 73, 2978, 10.1103/PhysRevLett.73.2978 Pomeau, 1983, Dislocation motion in cellular structures, Phys Rev A, 27, 2710, 10.1103/PhysRevA.27.2710 Peletier, 2003, Large time behaviour of solutions of the Swift-Hohenberg equation, R Acad Sci Paris Ser I, 336, 225, 10.1016/S1631-073X(03)00021-9 Vishal, 2012, Application of homotopy analysis method for fractional Swift Hohenberg equation - Revisited, Appl Math Model, 36, 3630, 10.1016/j.apm.2011.10.001 Khan, 2011, Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation, Comput Math Appl, 61, 2181, 10.1016/j.camwa.2010.09.009 Vishal, 2013, On the solutions of fractional Swift Hohenberg equation with dispersion, Appl Math Comput, 219, 5792, 10.1016/j.amc.2012.12.032 Li, 2018, An iterative method for time-fractional Swift-Hohenberg equation, Adv Math Phys, 2018, 10.1155/2018/2405432 Abdeljawad, 2017, On fractional derivatives with exponential kernel and their discrete versions, Rep Math Phys, 80, 11, 10.1016/S0034-4877(17)30059-9 Abdeljawad, 2016, Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels, Adv Diff, 2016, 232, 10.1186/s13662-016-0949-5 Refai, 2017, Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel, Adv Difference Equ, 2017, 315, 10.1186/s13662-017-1356-2 Jarad F, Abdeljawad T, Generalized fractional derivatives and Laplace transform. Discrete & Conti Dyn Sys S;2019:709. Kumar, 2014, Analytical solution of fractional Navier-Stokes equation by using modified Laplace decomposition method, Ain Shams Eng J, 5, 569, 10.1016/j.asej.2013.11.004 Singh J, Rashidi MM, Kumar D, Swroop R, A fractional model of a dynamical Brusselator reaction-diffusion system arising in triple collision and enzymatic reactions. Nonlinear Eng 2016;5(4):277–285. Khuri, 2001, A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J Appl Math, 1, 141, 10.1155/S1110757X01000183 Khan, 2010, Application of Laplace decomposition method to solve nonlinear coupled partial differential equations, World Appl Sci J, 9, 13 Ahmadian, 2017, A novel approach to approximate fractional derivative with uncertain conditions, Chaos Solitons Fractals, 104, 68, 10.1016/j.chaos.2017.07.026 Figueiredo Camargo, 2012, On the generalized Mittag-Leffler function and its application in a fractional telegraph equation, Math Phys Anal Geom, 15, 1, 10.1007/s11040-011-9100-8 Zhang, 2020, Periodic motion for impulsive fractional functional differential equations with piecewise Caputo derivative, Appl Math Lett, 101, 106072, 10.1016/j.aml.2019.106072 Ongun, 2011, The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4+T cells, Math Comput Model, 53, 597, 10.1016/j.mcm.2010.09.009 Wazwaz, 2010, The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations, Appl Math Comput, 216, 1304, 10.1016/j.amc.2010.02.023 Yusufoglu, 2006, Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl Math Comput, 177, 572, 10.1016/j.amc.2005.07.072 Odibat, 2006, Application of variational iteration method to nonlinear differential equation of fractional order, Int J Nonlinear Sci Numer Simul, 7, 27, 10.1515/IJNSNS.2006.7.1.27