...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 34 | Number 1 | Year 2016 | Article Id. IJMTT-V34P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V34P508

Picard,Adomian and Predictor-Corrector methods for integral equations of fractional order


W.K.Zahra, M.A.Shehata
Abstract

In this paper, a comparative study of Picard method, Adomian method and Predictor-Corrector method are presented for fractional integral equation. In Picard method [6] a uniform convergent solution for the fractional integral equation is obtained. Also, for Adomian method, we construct a series solution see ([1], [5] and [7]). Finally, Predictor-Corrector method is used for solving fractional integral equation. Two test problems are discussed to compare the maximum error for each method.

Keywords
Integral equation, Picard method, Adomian method, Predictor-Corrector method, Continuous unique solution, Fractional-order integration, Convergence analysis, Error analysis.
References

[1] G. Adomian, Stochastic System, Academic press, 1983.
[2] K Diethelm, A Freed, TheFrac.PECE subroutine for the numerical solution of differential equations of fractional order, in: S Heinzel, T Plesser (Eds.), Forschung and wissens chaftliches Rechnen 1998, Gesellschaftf AEur Wisses chaftliche Datenverar beitung, G"ottingen, 1999, pp 57-71.
[3] Diethelm, N J Ford and A D Freed. Predictor Corrector approach For the numerical solution of fractional differential equations, Nonlinear Dynamics, 29, 3- 22, 2002.
[4] K. Abbaoui, Y. Cherruault, Convergence of Adomian's method Applied to Differential Equations, Computers Math. Applic. 28 (1994) 103-109.
[5] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, 1995.
[6] N. Bellomo and D. Sarafyan, On Adomian's decomposition method and some comparisons with Picard's iterative scheme, Journal of Mathematical Analysis and Applications 123 (1987) 389-400.
[7] Y. Cherruault, Convergence of Adomian method, Kybernetes, 18 (1989) 31-38.
[8] C. Corduneanu, Principles of Differential and integral equations, Allyn and Bacon. Hnc, New Yourk, 1971.
[9] A. M. A. El-Sayed, H. H. G. Hashem, Integrable and continuous solutions of nonlinear quadratic integral equation, Electronic Journal of Qualitative Theory of Differential Equations 25 (2008) 1-10.
[10] A. M. A. El-Sayed, H. H. G. Hashem, Monotonic positive solution of nonlinear quadratic Hammerstein and Urysohn functional integral equations, Commentationes Mathematical. 48 (2) (2008) 199-207
[11] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, North-Holland, 2006
[12] I. Podlubny, Fractional Differential equations. San Diego-New York-London, 1999.
[13] B. Ross, K. S. Miller, an Introduction to Fractional Calculus and Fractional Differential Equations. John Wiley, New York, 1993

Citation :

W.K.Zahra, M.A.Shehata, "Picard,Adomian and Predictor-Corrector methods for integral equations of fractional order," International Journal of Mathematics Trends and Technology (IJMTT), vol. 34, no. 1, pp. 34-38, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V34P508

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved