On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay

[1]  Chang Phang,et al.  Operational matrix based on Genocchi polynomials for solution of delay differential equations , 2017, Ain Shams Engineering Journal.

[2]  Mingxu Yi,et al.  CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel , 2015, Int. J. Comput. Math..

[3]  Enrico Scalas,et al.  Waiting-times and returns in high-frequency financial data: an empirical study , 2002, cond-mat/0203596.

[4]  Mujeeb ur Rehman,et al.  Modified Chebyshev wavelet methods for fractional delay-type equations , 2015, Appl. Math. Comput..

[5]  A. Isah,et al.  Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations , 2016 .

[6]  Yadollah Ordokhani,et al.  A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations , 2016, Numerical Algorithms.

[7]  Reza Abazari,et al.  Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay , 2011, Int. J. Comput. Math..

[8]  J. Tanthanuch.  Symmetry analysis of the nonhomogeneous inviscid Burgers equation with delay , 2012 .

[9]  Xin Lu,et al.  Approximate inversion method for time‐fractional subdiffusion equations , 2018, Numer. Linear Algebra Appl..

[10]  Chang Phang,et al.  New operational matrix of derivative for solving non-linear fractional differential equations via Genocchi polynomials , 2017, Journal of King Saud University - Science.

[11]  Abbas Saadatmandi,et al.  Bernstein operational matrix of fractional derivatives and its applications , 2014 .

[12]  A. Nazemi,et al.  A New Approach for Solving a Class of Delay Fractional Partial Differential Equations , 2018, Mediterranean Journal of Mathematics.

[13]  Weiwei Zhao,et al.  Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations , 2010, Appl. Math. Comput..

[14]  R. Bagley,et al.  A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity , 1983 .

[15]  Rahmat Ali Khan,et al.  The Legendre wavelet method for solving fractional differential equations , 2011 .

[16]  Fevzi Erdogan,et al.  Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method , 2016 .

[17]  S. Haq,et al.  RBFs approximation method for time fractional partial differential equations , 2011 .

[18]  Svyatoslav I. Solodushkin,et al.  First order partial differential equations with time delay and retardation of a state variable , 2015, J. Comput. Appl. Math..

[19]  Hossein Jafari,et al.  Solving a multi-order fractional differential equation using adomian decomposition , 2007, Appl. Math. Comput..

[20]  A. Iserles,et al.  Stability of the discretized pantograph differential equation , 1993 .

[21]  Fengying Zhou,et al.  The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients , 2016, Appl. Math. Comput..

[22]  Yadollah Ordokhani,et al.  Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations , 2014 .

[23]  Esmail Babolian,et al.  Numerical solution of linear integro-differential equation by using sine-cosine wavelets , 2006, Appl. Math. Comput..

[24]  Jorge Eduardo Macías-Díaz,et al.  A novel discrete Gronwall inequality in the analysis of difference schemes for time-fractional multi-delayed diffusion equations , 2019, Commun. Nonlinear Sci. Numer. Simul..

[25]  Muthukumar Palanisamy,et al.  Numerical solution of fractional delay differential equation by shifted Jacobi polynomials , 2017, Int. J. Comput. Math..

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

[27]  Mehmet Sezer,et al.  Approximate solution of multi-pantograph equation with variable coefficients , 2008 .

[28]  Barbara Zubik-Kowal,et al.  Chebyshev pseudospectral method and waveform relaxation for differential and differential-functional parabolic equations , 2000 .

[29]  Yadollah Ordokhani,et al.  Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations , 2018, Numerical Algorithms.

[30]  I. Aziz,et al.  Numerical solution of a class of delay differential and delay partial differential equations via Haar wavelet , 2016 .

[31]  A. Bhrawy,et al.  A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations , 2013 .

[32]  J. A. Tenreiro Machado,et al.  Discrete-time fractional-order controllers , 2001 .

[33]  H. I. Freedman,et al.  Analysis of a model representing stage-structured population growth with state-dependent time delay , 1992 .

[34]  Saeed Kazem,et al.  Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation , 2015, Appl. Math. Comput..

[35]  Yuan-Ming Wang.  A high-order compact finite difference method and its extrapolation for fractional mobile/immobile convection–diffusion equations , 2017 .

[36]  Xiaoyun Jiang,et al.  Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition , 2009, Appl. Math. Comput..

[37]  Changpin Li,et al.  Numerical methods for fractional partial differential equations , 2018, Int. J. Comput. Math..

[38]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[39]  Z. Jackiewicz,et al.  Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations , 2006 .

[40]  S. Momani,et al.  Numerical comparison of methods for solving linear differential equations of fractional order , 2007 .

[41]  Alexei I. Zhurov,et al.  Functional constraints method for constructing exact solutions to delay reaction-diffusion equations and more complex nonlinear equations , 2014, Commun. Nonlinear Sci. Numer. Simul..

[42]  Mujeeb ur Rehman,et al.  Haar wavelet Picard method for fractional nonlinear partial differential equations , 2015, Appl. Math. Comput..

[43]  Rob H. De Staelen,et al.  A semi-linear delayed diffusion-wave system with distributed order in time , 2017, Numerical Algorithms.

[44]  Ahmed S. Hendy,et al.  A numerical solution for a class of time fractional diffusion equations with delay , 2017, Int. J. Appl. Math. Comput. Sci..

[45]  Serkan Araci,et al.  Some New Formulae for Genocchi Numbers and Polynomials Involving Bernoulli and Euler Polynomials , 2014, Int. J. Math. Math. Sci..

[46]  Eid H. Doha,et al.  A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order , 2011, Comput. Math. Appl..

[47]  Shaher Momani,et al.  Solving systems of fractional differential equations by homotopy-perturbation method , 2008 .

[48]  Muhammad Asad Iqbal,et al.  Modified Laguerre Wavelets Method for delay differential equations of fractional-order , 2015 .