On a numerical solution for fractional differential equation within B-spline operational matrix

In our manuscript we suggest an approach to obtain the solutions of the fractional differential equations(FDEs). We found the operational matrix within the linear B-spline functions. In this way the investigated equations are turned into a set of algebraic equations. We provide examples to illustrate both accuracy and simplicity of the suggested approach.

[1]  D. Baleanu,et al.  Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Fractional Evolution Equations , 2014 .

[2]  Dumitru Baleanu,et al.  A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations , 2014 .

[3]  D. Baleanu,et al.  The existence of solutions for a nonlinear mixed problem of singular fractional differential equations , 2013, Advances in Difference Equations.

[4]  D. Baleanu,et al.  Homotopy analysis method for solving Abel differential equation of fractional order , 2013 .

[5]  Saeed Kazem,et al.  Fractional-order Legendre functions for solving fractional-order differential equations , 2013 .

[6]  Sunil Kumar,et al.  Sunil Kumar , 2013 .

[7]  D. Baleanu,et al.  A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials , 2012 .

[8]  A. Bhrawy,et al.  An operational matrix of fractional integration of the Laguerre polynomials and its application on a semi-infinite interval , 2012 .

[9]  Xinxiu Li,et al.  Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method , 2012 .

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

[11]  Mehdi Dehghan,et al.  THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS , 2012 .

[12]  Mehdi Dehghan,et al.  A numerical technique for solving fractional optimal control problems , 2011, Comput. Math. Appl..

[13]  Andrew K. Chan,et al.  Fundamentals of Wavelets: Theory, Algorithms, and Applications , 2011 .

[14]  Mahmoud Behroozifar,et al.  Operational matrices of Bernstein polynomials and their applications , 2010, Int. J. Syst. Sci..

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

[16]  Hossein Jafari,et al.  SOLVING FRACTIONAL DIFFUSION AND WAVE EQUATIONS BY MODIFIED HOMOTOPY PERTURBATION METHOD , 2007 .

[17]  Pankaj Kumar,et al.  An approximate method for numerical solution of fractional differential equations , 2006, Signal Process..

[18]  M. Razzaghi,et al.  SEMIORTHOGONAL SPLINE WAVELETS APPROXIMATION FOR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS , 2006 .

[19]  Guanrong Chen,et al.  A note on the fractional-order Chen system , 2006 .

[20]  R. Gorenflo,et al.  Fractional calculus and continuous-time finance , 2000, cond-mat/0001120.

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

[22]  Jianzhong Wang,et al.  Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs , 1996 .

[23]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[24]  Alan Solomon,et al.  The initial-value problem for the equation (_{})_{}=ₓₓ , 1970 .