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Application of first integral method to fractional partial differential equations

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Abstract

In this paper, fractional derivatives in the sense of modified Riemann-Liouville derivative and first integral method are applied for constructing exact solutions of nonlinear fractional generalized reaction duffing model and nonlinear fractional diffusion reaction equation with quadratic and cubic nonlinearity. Our approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solutions are constructed through established first integrals.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    M. Eslami

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    B. Fathi Vajargah & M. Mirzazadeh

  3. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA

    A. Biswas

  4. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    A. Biswas

Authors
  1. M. Eslami
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  2. B. Fathi Vajargah
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  3. M. Mirzazadeh
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  4. A. Biswas
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Corresponding author

Correspondence to M. Mirzazadeh.

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Eslami, M., Fathi Vajargah, B., Mirzazadeh, M. et al. Application of first integral method to fractional partial differential equations. Indian J Phys 88, 177–184 (2014). https://doi.org/10.1007/s12648-013-0401-6

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  • DOI: https://doi.org/10.1007/s12648-013-0401-6

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