A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations

[1]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[2]  I. Podlubny.  Fractional differential equations , 1998 .

[3]  E. E. Doha,et al.  On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations , 2002 .

[4]  N. Ford,et al.  The numerical solution of linear multi-term fractional differential equations: systems of equations , 2002 .

[5]  E. H. Doha.  Explicit Formulae for the Coefficients of Integrated Expansions of Jacobi Polynomials and Their Integrals , 2003 .

[6]  Kai Diethelm,et al.  Efficient Solution of Multi-Term Fractional Differential Equations Using P(EC)mE Methods , 2003, Computing.

[7]  Kai Diethelm,et al.  Multi-order fractional differential equations and their numerical solution , 2004, Appl. Math. Comput..

[8]  Ahmed M. A. El-Sayed,et al.  Numerical methods for multi-term fractional (arbitrary) orders differential equations , 2005, Appl. Math. Comput..

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

[10]  R. Magin.  Fractional Calculus in Bioengineering , 2006 .

[11]  Weihua Deng,et al.  Short memory principle and a predictor-corrector approach for fractional differential equations , 2007 .

[12]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[13]  Ali H. Bhrawy,et al.  A Jacobi spectral Galerkin method for the integrated forms of fourth‐order elliptic differential equations , 2009 .

[14]  Neville J. Ford,et al.  Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations , 2009 .

[15]  Mehdi Dehghan,et al.  A new operational matrix for solving fractional-order differential equations , 2010, Comput. Math. Appl..

[16]  Lifeng Ma,et al.  Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations , 2010, Appl. Math. Lett..

[17]  M. Amairi,et al.  A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation , 2010, Appl. Math. Comput..

[18]  Ali H. Bhrawy,et al.  A quadrature tau method for fractional differential equations with variable coefficients , 2011, Appl. Math. Lett..

[19]  Hossein Jafari,et al.  Application of Legendre wavelets for solving fractional differential equations , 2011, Comput. Math. Appl..

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

[21]  E. H. Doha,et al.  EFFICIENT CHEBYSHEV SPECTRAL METHODS FOR SOLVING MULTI-TERM FRACTIONAL ORDERS DIFFERENTIAL EQUATIONS , 2011 .

[22]  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..

[23]  M. Shamsi,et al.  A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations , 2011 .

[24]  Eid H. Doha,et al.  Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations , 2011, Appl. Math. Lett..

[25]  Arvet Pedas,et al.  Spline collocation methods for linear multi-term fractional differential equations , 2011, J. Comput. Appl. Math..

[26]  Neville J. Ford,et al.  Fractional boundary value problems: Analysis and numerical methods , 2011 .

[27]  Ali H Bhrawy,et al.  A shifted Legendre spectral method for fractional-order multi-point boundary value problems , 2012 .

[28]  Yanxin Wang,et al.  The second kind Chebyshev wavelet method for solving fractional differential equations , 2012, Appl. Math. Comput..

[29]  Arvet Pedas,et al.  Piecewise polynomial collocation for linear boundary value problems of fractional differential equations , 2012, J. Comput. Appl. Math..

[30]  M. Rehman,et al.  A numerical method for solving boundary value problems for fractional differential equations , 2012 .

[31]  E. H. Doha,et al.  A NEW JACOBI OPERATIONAL MATRIX: AN APPLICATION FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS , 2012 .

[32]  Ali H. Bhrawy,et al.  The operational matrix of fractional integration for shifted Chebyshev polynomials , 2013, Appl. Math. Lett..