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Mathematical Problems in Engineering
Volume 2012, Article ID 329575, 11 pages
http://dx.doi.org/10.1155/2012/329575
Research Article

A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

1Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China
2State key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received 28 April 2012; Accepted 11 July 2012

Academic Editor: Hung Nguyen-Xuan

Copyright © 2012 Er Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. J. Wu and Y. Liu, “Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces,” Electronic Journal of Differential Equations, no. 129, pp. 1–8, 2009. View at Google Scholar · View at Zentralblatt MATH
  3. S. Hamani, M. Benchohra, and J. R. Graef, “Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions,” Electronic Journal of Differential Equations, no. 20, pp. 1–16, 2010. View at Google Scholar · View at Scopus
  4. B. Ahmad and S. Sivasundaram, “On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 480–487, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. G. J. Fix and J. P. Roop, “Least squares finite-element solution of a fractional order two-point boundary value problem,” Computers & Mathematics with Applications, vol. 48, no. 7-8, pp. 1017–1033, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. E. A. Rawashdeh, “Numerical solution of fractional integro-differential equations by collocation method,” Applied Mathematics and Computation, vol. 176, no. 1, pp. 1–6, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. Arikoglu and I. Ozkol, “Solution of fractional integro-differential equations by using fractional differential transform method,” Chaos, Solitons and Fractals, vol. 40, no. 2, pp. 521–529, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. S. Momani and R. Qaralleh, “Numerical approximations and Padé approximants for a fractional population growth model,” Applied Mathematical Modelling, vol. 31, no. 9, pp. 1907–1914, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. Odibat and S. Momani, “Numerical solution of Fokker-Planck equation with space- and time-fractional derivatives,” Physics Letters, Section A, vol. 369, no. 5-6, pp. 349–358, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Momani and M. Aslam Noor, “Numerical methods for fourth-order fractional integro-differential equations,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 754–760, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. Momani and R. Qaralleh, “An efficient method for solving systems of fractional integro-differential equations,” Computers & Mathematics with Applications, vol. 52, no. 3-4, pp. 459–470, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. Long and X. Zhang, “Construction and calculation of reproducing kernel determined by various linear differential operators,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 759–766, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Y. Lin and J. Lin, “Numerical method for solving the nonlinear four-point boundary value problems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 3855–3864, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. X. J. Zhang and H. Long, “Computing reproducing kernels for W2m[a,b]. I,” Mathematica Numerica Sinica, vol. 30, no. 3, pp. 295–304, 2008. View at Google Scholar
  15. M. Cui and Z. Chen, “The exact solution of nonlinear age-structured population model,” Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1096–1112, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH