A new efficient algorithm based on fifth-kind Chebyshev polynomials for solving multi-term variable-order time-fractional diffusion-wave equation

[1]  Mohammad Hossein Heydari,et al.  A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation , 2019, Appl. Math. Comput..

[2]  Ben-yu Guo,et al.  Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces , 2004, J. Approx. Theory.

[3]  Dov Ingman,et al.  Control of damping oscillations by fractional differential operator with time-dependent order , 2004 .

[4]  M. Heydari,et al.  Numerical solution of variable-order space-time fractional KdV–Burgers–Kuramoto equation by using discrete Legendre polynomials , 2020, Engineering with Computers.

[5]  YangQuan Chen,et al.  A Physical experimental study of variable-order fractional integrator and differentiator , 2011 .

[6]  Dominik Sankowski,et al.  Order Functions Selection in the Variable-, Fractional-Order PID Controller , 2014, RRNR.

[7]  E. H. Doha,et al.  Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains , 2020 .

[8]  A. Borhanifar,et al.  A generalized operational method for solving integro–partial differential equations based on Jacobi polynomials , 2016 .

[9]  Carlos F.M. Coimbra,et al.  A variable order constitutive relation for viscoelasticity , 2007 .

[10]  Huan Liu,et al.  A two-grid MMOC finite element method for nonlinear variable-order time-fractional mobile/immobile advection-diffusion equations , 2020, Comput. Math. Appl..

[11]  Youssri Hassan Youssri,et al.  Spectral Solutions for Fifth-Order Boundary Value Problems Using Generalized Jacobi Operational Matrix of Derivatives , 2017 .

[12]  B. Ross,et al.  Integration and differentiation to a variable fractional order , 1993 .

[13]  Zakieh Avazzadeh,et al.  A new Wavelet Method for Variable‐Order Fractional Optimal Control Problems , 2018 .

[14]  Yi-Ming Chen,et al.  Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets , 2015, Appl. Math. Lett..

[15]  Y. H. Youssri,et al.  Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations , 2018 .

[16]  Fawang Liu,et al.  Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain , 2012, Comput. Math. Appl..

[17]  W. Zahra,et al.  Non standard finite difference method for solving variable order fractional optimal control problems , 2017 .

[18]  R. Nigmatullin To the Theoretical Explanation of the “Universal Response” , 1984 .

[19]  E. H. Doha,et al.  On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain , 2018, Nonlinear Engineering.

[20]  R. Nigmatullin The Realization of the Generalized Transfer Equation in a Medium with Fractal Geometry , 1986, January 1.

[21]  Zakieh Avazzadeh,et al.  An operational matrix method for solving variable-order fractional biharmonic equation , 2018 .

[22]  Ali H. Bhrawy,et al.  Numerical algorithm for the variable-order Caputo fractional functional differential equation , 2016 .

[23]  Youssri Hassan Youssri,et al.  Sixth-Kind Chebyshev Spectral Approach for Solving Fractional Differential Equations , 2019, International Journal of Nonlinear Sciences and Numerical Simulation.

[24]  R. Hafez,et al.  Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis , 2019, Arabian Journal of Mathematics.

[25]  Carlos F.M. Coimbra,et al.  Mechanics with variable‐order differential operators , 2003 .

[26]  M. Heydari,et al.  Discrete Chebyshev polynomials for nonsingular variable‐order fractional KdV Burgers' equation , 2020, Mathematical Methods in the Applied Sciences.

[27]  Mohammad Hossein Heydari,et al.  A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems , 2018, J. Frankl. Inst..

[28]  M. Heydari,et al.  Legendre wavelets optimization method for variable-order fractional Poisson equation , 2018, Chaos, Solitons & Fractals.

[29]  M. R. Hooshmandasl,et al.  A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation , 2020, Mathematical Methods in the Applied Sciences.

[30]  Carlos F.M. Coimbra,et al.  The variable viscoelasticity oscillator , 2005 .

[31]  Shyam L. Kalla,et al.  Fractional extensions of the temperature field problems in oil strata , 2007, Appl. Math. Comput..

[32]  M. Heydari,et al.  Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system , 2020, Engineering with Computers.

[33]  Hong Wang,et al.  A variable-order fractional differential equation model of shape memory polymers , 2017 .

[34]  Abdon Atangana,et al.  An optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels , 2020 .