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Solution of nonlinear fractional differential equations using an efficient approach

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Abstract

We present an efficient approach for solving nonlinear fractional differential equations. The convergence analysis of the approach is studied. To demonstrate the working of the presented approach, we consider three special cases of nonlinear fractional differential equations. The results of theses examples and comparison with different methods provide confirmation for the validity of the proposed approach.

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References

  1. Luchko AY, Groreflo R (1998) The initial value problem for some fractional differential equations with the Caputo derivative, Preprint series A08-98, Fachbreich Mathematik und Informatik, Freic Universitat Berlin

  2. Gorenflo R, Mainardi F (1997) Fractional calculus: integral and differential equations of fractional order. In: Carpinteri A, Mainardi F (eds) Fractals and fractional calculus in continuum mechanics. Springer, New York

    Google Scholar 

  3. Podlubny I, El-Sayed AMA (1996) On two definitions of fractional calculus. Solvak Academy of science-institute of experimental phys. UEF-03-96 ISBN 80-7099-252-2

  4. Podlubny I (1999) Fractional differential equations. Academic Press, New York

    MATH  Google Scholar 

  5. Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent. Part II J R Astral Soc 13:529–539

    Google Scholar 

  6. Mainardi F (1994) On the initial value problem for the fractional diffusion-wave equation. In: Rionero S, Ruggeeri T (eds) Waves and stability in continuous media. World Scientific, Singapore, pp 246–51

    Google Scholar 

  7. Das S, Vishal K, Gupta PK (2011) Solution of the nonlinear fractional diffusion equation with absorbent term and external force. Appl Math Model 35:3970–3979

    Article  MATH  MathSciNet  Google Scholar 

  8. Das S, Gupta PK, Ghosh P (2011) An approximate solution of nonlinear fractional reaction-diffusion equation. Appl Math Model 35:4071–4076

    Article  MATH  MathSciNet  Google Scholar 

  9. Gupta PK, Singh J, Rai KN (2010) Numerical simulation for heat transfer in tissues during thermal therapy. J Therm Biol 35:295–301

    Article  Google Scholar 

Download references

Acknowledgment

This research was partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Iran.

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Correspondence to Y. Khan.

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Khan, Y., Fardi, M., Sayevand, K. et al. Solution of nonlinear fractional differential equations using an efficient approach. Neural Comput & Applic 24, 187–192 (2014). https://doi.org/10.1007/s00521-012-1208-7

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  • DOI: https://doi.org/10.1007/s00521-012-1208-7

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