Exact solutions for some of the fractional integro-differential equations with the nonlocal boundary conditions by using the modification of He’s variational iteration method

Authors and Affiliations

  • Safar Irandoust-pakchin
  • Somayeh Abdi-mazraeh

About this article

Download PDF

Keywords:

Fractional integro-difierential equations, nonlocal boundary condition, modiflcation of He’s variational iteration method.

Abstract

In this paper, the modification of He's variational iteration method (MVIM) is developed to solve fractional integro-differential equations with nonlocal boundary conditions. It is shown that by choosing suitable initial approximation, the exact solution obtains by one iteration. It is illustrated that the propose method is effective and has high convergency rate.


References

A. Arikoglu, I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform

method, Chaos, Solitons and Fractals (2007).

A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien, New

York, 1997.

K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Electron. Trans.

View more references (33)

Numer. Anal. 5 (1997) 1-6.

A. Ghorbani, J. Saberi-Nadjafl, An effective modification of He’s variational iteration method, Nonlinear Analysis: Real

World Applications 10 (2009) 2828{2833.

R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, in: A. Carpinteri,

F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York, 1997, pp. 223-276.

J. H. He, Some applications of nonlinear fractional difierential equation and their approximations, Bull. Sci. Technol.

(12) (1999) 86-90.

J. H. He, X .H. Wu, Variational iteration method for autonomous ordinary difierential systems, Appl. Math. Comput.

(2000) 115-123.

J. H. He , Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul. 2 (4)

(1997) 235-236.

J. H. He, Variational iteration method: New development and applications, Comput. Math. Appl. doi:10.1016/j.camwa.

12.083.

J. H. He, Variational iteration method-Some recent results and new interpretations, J. Comput. Appl. Math, 207 (2007)

-17.

F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, in: A. Carpinteri, F.

Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York, 1997, pp. 291-348.

S. Momani, M. A. Noor, Numerical methods for fourth-order fractional integro-differential equations, Appl. Math.

Comput, 182 (2006) 754{60.

D. Nazari , S. Shahmorad, Application of fractional differential transform method to the fractional order integro-differential equations with nonlocal boundary condition, J. Comput. Appl. Math, (2010), doi:10.1016/j.cam.2010.01.053.

Z. M. Odibat, A study on the convergence of the variational iteration method, Mathematical and Computer Modelling

(2010), doi:10.1016/j.mcm.2009.12.034.

K .B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.

E. A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math.

Comput., 176 (2006) 1-6.

M. Tatari, M. Dehghan, On the convergence of He’s variational iteration method, J. Comput. Appl. Math. 207 (2007)

-128.

S. Q. Wang , J. H. He, Variational iteration method for solving integro-difierential equations, Phys. Lett. A 367 (2007)

-191.

L. Xu, Variational iteration method for solving integral equations, Comput. Math. Appl.

doi:10.1016/j.camwa.(2006).12.053.

R. Yulita Molliq, M. S. M. Noorani, I. Hashim, Variational iteration method for fractional heat- and wave-like equations,

Nonlinear Analysis: Real World Applications 10 (2009) 1854-1869.


How to Cite

Irandoust-pakchin, S., & Abdi-mazraeh, S. (2013). Exact solutions for some of the fractional integro-differential equations with the nonlocal boundary conditions by using the modification of He’s variational iteration method. International Journal of Advanced Mathematical Sciences, 1(3), 139-144. https://doi.org/10.14419/ijams.v1i3.983