Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speed , electron number density (through ) and the fractional order on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.

[1]  Tonghua Zhang,et al.  Periodic Solution and Ergodic Stationary Distribution of SEIS Dynamical Systems with Active and Latent Patients , 2018, Qualitative Theory of Dynamical Systems.

[2]  Jinliang Zhang,et al.  Decay mode solutions to cylindrical KP equation , 2016, Appl. Math. Lett..

[3]  G. Murtaza,et al.  Ion-acoustic solitary waves in ultra-relativistic degenerate pair-ion plasmas , 2011 .

[4]  Lei Fu,et al.  An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves , 2019, Complex..

[5]  Hongwei Yang,et al.  The time-fractional mZK equation for gravity solitary waves and solutions using sech-tanh and radial basis function method , 2018, Nonlinear Analysis: Modelling and Control.

[6]  Shu-fang Deng,et al.  The decay mode solutions for the cylindrical KP equation , 2012, Appl. Math. Comput..

[7]  Hongwei Yang,et al.  Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids , 2019, Mathematics.

[8]  S. Ege,et al.  A new method for solving nonlinear fractional differential equations , 2017 .

[9]  Om P. Agrawal,et al.  Formulation of Euler–Lagrange equations for fractional variational problems , 2002 .

[10]  Om P. Agrawal,et al.  Fractional variational calculus and the transversality conditions , 2006 .

[11]  Ruigang Zhang,et al.  A new model equation for nonlinear Rossby waves and some of its solutions , 2019, Physics Letters A.

[12]  Ahmet Bekir,et al.  A novel analytical method for time-fractional differential equations , 2016 .

[13]  Muhammad Adil Khan,et al.  Generalized conformable fractional operators , 2019, J. Comput. Appl. Math..

[14]  Abdullah Al Mamun,et al.  Nonplanar dust ion-acoustic solitary and shock waves in a dusty plasma with electrons following a vortex-like distribution , 2010 .

[15]  Yadollah Ordokhani,et al.  Fractional-order Legendre-Laguerre functions and their applications in fractional partial differential equations , 2018, Appl. Math. Comput..

[16]  B. Tian,et al.  Dust ion-acoustic rogue waves in a three-species ultracold quantum dusty plasmas , 2014 .

[17]  S. Chandrasekhar.  XLVIII. The density of white dwarf stars , 1931 .

[18]  Mustafa Inç,et al.  The First Integral Method for the time fractional Kaup-Boussinesq System with time dependent coefficient , 2015, Appl. Math. Comput..

[19]  郑滨.  (G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics , 2012 .

[20]  Hongwei Yang,et al.  Modeling and analysis of fractional neutral disturbance waves in arterial vessels , 2019, Mathematical Modelling of Natural Phenomena.

[21]  The maximum mass of ideal white dwarfs , 1931 .

[22]  Chen Fu,et al.  Time-fractional Benjamin-Ono equation for algebraic gravity solitary waves in baroclinic atmosphere and exact multi-soliton solution as well as interaction , 2019, Commun. Nonlinear Sci. Numer. Simul..

[23]  Yuansheng Tian,et al.  Multiplicity for fractional differential equations with p-Laplacian , 2018, Boundary Value Problems.

[24]  B. Warner,et al.  The Gravity Oscillations of White Dwarfs , 1975 .

[25]  Qasem M. Al-Mdallal,et al.  Fractional-order Legendre-collocation method for solving fractional initial value problems , 2018, Appl. Math. Comput..

[26]  Hongwei Yang,et al.  (3 + 1)‐Dimensional time‐fractional modified Burgers equation for dust ion‐acoustic waves as well as its exact and numerical solutions , 2019, Mathematical Methods in the Applied Sciences.

[27]  G. Jumarie,et al.  Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results , 2006, Comput. Math. Appl..

[28]  R. Sabry,et al.  Formation and dynamics of electrostatic solitary waves associated with relativistic electron beam , 2012 .

[29]  Yaning Tang,et al.  Double Wronskian solutions to the (2+1)-dimensional Broer-Kaup-Kupershmidt equation , 2020, Appl. Math. Lett..

[30]  Ata-ur-Rahman,et al.  Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas , 2013 .

[31]  Ji-Huan He,et al.  Fractal calculus and its geometrical explanation , 2018, Results in Physics.

[32]  Bo Tian,et al.  Cosmic dust-ion-acoustic waves, spherical modified Kadomtsev-Petviashvili model, and symbolic computation , 2006 .

[33]  P. Shukla,et al.  Ion-acoustic solitary waves in a dense pair-ion plasma containing degenerate electrons and positrons , 2008 .

[34]  Abdullah Al Mamun,et al.  Arbitrary amplitude solitary waves and double layers in an ultra-relativistic degenerate dense dusty plasma , 2010 .

[35]  M. Sababheh,et al.  A new definition of fractional derivative , 2014, J. Comput. Appl. Math..

[36]  S. El-Tantawy,et al.  Cylindrical freak waves in a non-Maxwellian dusty bulk-sheath plasma: An approximate solution for the cylindrical nonlinear Schrödinger equation , 2017 .

[37]  Ryogo Hirota,et al.  Exact solutions to the equation describing “cylindrical solitons” , 1979 .

[38]  A. Mushtaq.  Cylindrical dust acoustic solitary waves with transverse perturbations in quantum dusty plasmas , 2007 .

[39]  Hongwei Yang,et al.  Two-dimensional fractional algebraic internal solitary waves model and its solution , 2019, Advances in Mechanical Engineering.

[40]  Yong Zhang,et al.  Study of Ion-Acoustic Solitary Waves in a Magnetized Plasma Using the Three-Dimensional Time-Space Fractional Schamel-KdV Equation , 2018, Complex..

[41]  A. Córsico,et al.  A white dwarf cooling age of 8 Gyr for NGC 6791 from physical separation processes , 2010, Nature.

[42]  Xiaojun Yin,et al.  Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography , 2019, Appl. Math. Comput..

[43]  Detlev Koester,et al.  Physics of white dwarf stars , 1990 .

[44]  S. Chandrasekhar.  The maximum mass of ideal white dwarfs , 1931 .

[45]  N. Dangelo.  Dust acoustic waves excited by gravity in a collisional plasma , 2002 .

[46]  Yang Hong-wei,et al.  Fractional order model and Lump solution in dusty plasma , 2019, Acta Physica Sinica.

[47]  Zheng Bin,et al.  （G＇/G）-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics , 2012 .