Skip to main content
SpringerLink
Log in

An Application of ANNs Method for Solving Fractional Fredholm Equations

  • Conference paper
  • First Online:
Mendel 2015 (ICSC-MENDEL 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 378))

Included in the following conference series:

Abstract

‎For the last decade‎, ‎several authors demonstrated the performance‎ of artificial neural network models over other traditional testing‎ methods‎. ‎The current research‎, ‎aimed to present a global‎ optimization technique based on combination of neural networks‎ approach and power series method for the numerical solution of a‎ fractional Fredholm type integro-differential equation involving‎ the Caputo derivative‎. ‎In other words‎, ‎an‎ ‎accurate truncated power series representation of the solution‎ function is achieved when a suitable learning algorithm is used‎ for the suggested neural architecture‎. ‎As applications of the‎ present iterative approach‎, ‎some kinds of integro-differential‎ equations are investigated‎. ‎The achieved simulations are compared‎ with the results obtained by some existing algorithms‎.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anguraj, A., Karthikeyan, P., Rivero, M., Trujillo, J.J.: On new existence results for fractional integro-differential equations with impulsive and integral conditions 66(12), 2587–2594 (2014)

    MathSciNet  Google Scholar 

  2. Bandyopadhyay, B., Kamal, S.: Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach, vol. 317 (2015)

    Google Scholar 

  3. Graupe, D.: Principles of Artificial Neural Networks, 2nd edn. World Scientific, River Edge (2007)

    Google Scholar 

  4. Hanss, M.: Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Springer, Berlin (2005)

    Google Scholar 

  5. Huang, L., Li, X.F., Zhao, Y.L., Duan, X.Y.: Approximate solution of fractional integro-differential equations by Taylor expansion method. Comput. Math Appl. 62(3), 1127–1134 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Jafarian, A., Measoomy, S., Nia, S.: Abbasbandy, artificial neural networks based modeling for solving linear Volterra integral equations system. Appl. Soft Comput. 27, 391–395 (2015)

    Article  Google Scholar 

  7. Jafarian, A., Measoomy Nia, S.: Artificial neural network approach to the fuzzy Abel integral equation problem. J. Intell. Fuzzy Syst. doi:10.3233/IFS-130980

  8. Jafarian, A., Measoomy Nia, S.: New itrative method for solving linear Fredholm fuzzy integral equations of the second kined. Int. J. Ind. Math. 5(3), 10 pp (2013)

    Google Scholar 

  9. Jafarian, A., Measoomy Nia, S.: Feed-back neural network method for solving linear Volterra integral equations of the second kind. Int. J. Math. Modell. Numer. Optim. 4(3), 225–237 (2013)

    Google Scholar 

  10. Jafarian, A., Measoomy Nia, S.: Utilizing feed-back neural network approach for solving linear Fredholm integral equations system. Appl. Math. Modell. 37(7), 5027–5038 (2013)

    Google Scholar 

  11. Jumarie, G.: Modi_ed Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51 (2006)

    Google Scholar 

  12. Momani, S.M., Hadid, S.B.: Some comparison results for integro-fractional differential inequalities. J. Fract. Calc. 24, 37–44 (2003)

    MATH  MathSciNet  Google Scholar 

  13. Momani, S., Noor, M.: Numerical methods for fourth order fractional integro-differential equations. Appl. Math. Comput. 182, 754–760 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Nawaz, Y.: Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations. Comput. Math Appl. 61(8), 2330–2341 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Odibat, Z., Shawagfeh, N.: Generalized Taylors formula. Appl. Math. Comput. 186(1), 286–293 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ordokhani, Y., Rahimi, N.: Solving fractional nonlinear Fredholm integro-differential equations via hybrid of rationalized Haar functions. J. Inf. Comput. Sci. 9(3), 169–180 (2014)

    Google Scholar 

  17. Ray, S.S.: Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method. Commun. Nonlinear. Sci. Numer Simul. 14, 129–306 (2009)

    Google Scholar 

  18. Yang, X.J.: Advanced Local Fractional Calculus and Its Applications. World Science Publisher, New York, USA (2012)

    Google Scholar 

  19. Zhanga, L., Ahmadb, B., Wanga, G., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)

    Article  MathSciNet  Google Scholar 

  20. Zhu, L., Fan, Q.: Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet. Commun. Nonlinear Sci. Numer. Simul. 17, 2333–2341 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran

    Ahmad Jafarian

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Urmia, Iran

    S. Measoomy Nia

Authors
  1. Ahmad Jafarian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Measoomy Nia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmad Jafarian .

Editor information

Editors and Affiliations

  1. Faculty of Mechanical Engineering, Department of Applied Computer Science, Brno University of Technology, Brno, Czech Republic

    Radek Matoušek

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Jafarian, A., Measoomy Nia, S. (2015). An Application of ANNs Method for Solving Fractional Fredholm Equations. In: Matoušek, R. (eds) Mendel 2015. ICSC-MENDEL 2016. Advances in Intelligent Systems and Computing, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-319-19824-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19824-8_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19823-1

  • Online ISBN: 978-3-319-19824-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation