The analytical analysis of nonlinear fractional-order dynamical models

1 School of Mathematics and Information Sciences, Neijiang Normal University, 641112, Sichuan Province, China 2 Department of Mathematics Abdul Wali Khan University Mardan (AWKUM), Pakistan 3 Department of Mathematics, Near East University TRNC, Mersin 10, Turkey 4 Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Kingdom of Saudi Arabia 5 Department of Mathematics, Faculty of Science, AL-Azhar University, Assiut, 71516, Egypt 6 Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey 7 Institute of Space Sciences, Magurele-Bucharest, Romania

[1]  A. Newell,et al.  Swift-Hohenberg equation for lasers. , 1994, Physical review letters.

[2]  Rahmat Ali Khan,et al.  Numerical treatment for traveling wave solutions of fractional Whitham-Broer-Kaup equations , 2018, Alexandria Engineering Journal.

[3]  Muhammad Arif,et al.  Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations , 2019, Entropy.

[4]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[5]  H. Sakaguchi,et al.  Localized patterns for the quintic complex Swift—Hohenberg equation , 1998 .

[6]  Infinite Existence Solutions of Fractional Systems with Lipschitz Nonlinearity , 2020 .

[7]  K. Vishal,et al.  Application of homotopy analysis method for fractional Swift Hohenberg equation – Revisited , 2012 .

[8]  Mostafa M. A. Khater,et al.  A New Numerical Approach for Solving 1D Fractional Diffusion-Wave Equation , 2021 .

[9]  Saeid Abbasbandy,et al.  Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation , 2018, Appl. Math. Comput..

[10]  Robert A. Van Gorder,et al.  Analytical and numerical results for the Swift-Hohenberg equation , 2010, Appl. Math. Comput..

[11]  Z. Odibat,et al.  Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates , 2018, Nonlinear Dynamics.

[12]  Dianchen Lu,et al.  On the numerical investigation of the interaction in plasma between (high & low) frequency of (Langmuir & ion-acoustic) waves , 2020 .

[13]  Abdul-Majid Wazwaz,et al.  A reliable modification of Adomian decomposition method , 1999, Appl. Math. Comput..

[14]  Mostafa M. A. Khater,et al.  Diverse novel analytical and semi-analytical wave solutions of the generalized (2+1)-dimensional shallow water waves model , 2021 .

[15]  Suheil A. Khuri,et al.  A Laplace decomposition algorithm applied to a class of nonlinear differential equations , 2001 .

[16]  Wenjin Li,et al.  An Iterative Method for Time-Fractional Swift-Hohenberg Equation , 2018, Advances in Mathematical Physics.

[17]  Omar Abu Arqub,et al.  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 , 2017, Comput. Math. Appl..

[18]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[19]  Salah Boulaaras,et al.  Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique , 2021 .

[20]  Michael Defoort,et al.  Predefined-time convergence in fractional-order systems , 2021 .

[21]  Nikolai A. Kudryashov,et al.  Exact solutions of the Swift–Hohenberg equation with dispersion , 2011, 1112.5444.

[22]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[23]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[24]  Omar Abu Arqub,et al.  Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm , 2018 .

[25]  S. Boulaaras,et al.  On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity , 2020, Boundary Value Problems.

[26]  Scott G. McCalla,et al.  Snaking of radial solutions of the multi-dimensional Swift–Hohenberg equation: A numerical study , 2010 .

[27]  Muhammad Arif,et al.  Laplace Adomian Decomposition Method for Multi Dimensional Time Fractional Model of Navier-Stokes Equation , 2019, Symmetry.

[28]  F. Mainardi Fractional Calculus , 2018, Fractional Calculus.

[29]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[30]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[31]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[32]  Muhammad Arif,et al.  Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method , 2019, Entropy.

[33]  N. Mehmood,et al.  Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions , 2020 .

[34]  M. Arif,et al.  Approximate solutions to nonlinear factional order partial differential equations arising in ion-acoustic waves , 2019, AIMS Mathematics.

[35]  Dumitru Baleanu,et al.  An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations , 2019, Mathematics.

[36]  Junqiang Song,et al.  A General Iteration Formula of VIM for Fractional Heat- and Wave-Like Equations , 2013, J. Appl. Math..

[37]  P. Hohenberg,et al.  Effects of additive noise at the onset of Rayleigh-Bénard convection. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[38]  Najeeb Alam Khan,et al.  Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation , 2011, Comput. Math. Appl..

[39]  N. Raza,et al.  Unsteady magneto-hydrodynamics flow between two orthogonal moving porous plates , 2019, The European Physical Journal Plus.

[40]  F. Haq,et al.  Application of a hybrid method for systems of fractional order partial differential equations arising in the model of the one-dimensional Keller-Segel equation , 2019, The European Physical Journal Plus.

[41]  Sim Heng Ong,et al.  On the solutions of fractional Swift Hohenberg equation with dispersion , 2013, Appl. Math. Comput..

[42]  M. Merdan A numeric–analytic method for time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative , 2013 .