An efficient scheme for solving a system of fractional differential equations with boundary conditions

[1]  Andrew Resnick,et al.  Fractional calculus: an introduction for physicists, 3rd edition , 2019, Contemporary Physics.

[2]  Wei Zhao,et al.  A new definition of fractional derivative , 2019, International Journal of Non-Linear Mechanics.

[3]  J. Machado,et al.  EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN , 2017 .

[4]  Xiao‐Jun Yang,et al.  Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems , 2016, 1612.03202.

[5]  J. Machado,et al.  A new fractional operator of variable order: Application in the description of anomalous diffusion , 2016, 1611.09200.

[6]  Obaid J. Algahtani,et al.  Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model , 2016 .

[7]  M. Rawashdeh,et al.  Numerical Solutions for Systems of Nonlinear Fractional Ordinary Differential Equations Using the FNDM , 2016 .

[8]  A. Atangana,et al.  New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model , 2016, 1602.03408.

[9]  J. A. Tenreiro Machado,et al.  A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow , 2015, 1601.01623.

[10]  Sertan Alkan A new solution method for nonlinear fractional integro-differential equations , 2015 .

[11]  Esmail Hesameddini,et al.  Numerical solution of multi-order fractional differential equations via the sinc collocation method , 2015 .

[12]  Sertan Alkan,et al.  Solving nonlinear boundary value problems by the Galerkin method with sinc functions , 2015 .

[13]  R. P. Meilanov,et al.  Thermodynamics in Fractional Calculus , 2014 .

[14]  Abdon Atangana,et al.  Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems , 2014 .

[15]  Pietro Cornetti,et al.  Nonlocal elasticity: an approach based on fractional calculus , 2014, Meccanica.

[16]  M. Bayram,et al.  Sinc-Galerkin method for approximate solutions of fractional order boundary value problems , 2013 .

[17]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[18]  O. P. Singh,et al.  An Analytic Algorithm for Solving System of Fractional Differential Equations , 2011 .

[19]  N. Khan,et al.  On Efficient Method for System of Fractional Differential Equations , 2011 .

[20]  Dumitru Baleanu,et al.  On nonlinear fractional Klein-Gordon equation , 2011, Signal Process..

[21]  R. Herrmann Fractional Calculus: An Introduction for Physicists , 2011 .

[22]  Dumitru Baleanu,et al.  Fractional Newtonian mechanics , 2010 .

[23]  Hossein Jafari,et al.  SOLVING A SYSTEM OF NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS USING HOMOTOPY ANALYSIS METHOD , 2009 .

[24]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[25]  Mohamed El-Gamel,et al.  On the Galerkin and collocation methods for two-point boundary value problems using sinc bases , 2008, Comput. Math. Appl..

[26]  S. Momani,et al.  Solving systems of fractional differential equations using differential transform method , 2008 .

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

[28]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[29]  Hossein Jafari,et al.  Solving a system of nonlinear fractional differential equations using Adomian decomposition , 2006 .

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

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

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

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

[34]  Aydin Seçer,et al.  An efficient algorithm for solving fractional differential equations with boundary conditions , 2016 .

[35]  S. Arabia,et al.  LOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR DIFFUSION AND WAVE EQUATIONS ON CANTOR SETS , 2014 .

[36]  Jun-Sheng Duan,et al.  Solution of system of fractional differential equations by Adomian decomposition method , 2007 .

[37]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[38]  H. Kober ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .