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Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method

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  • Fanwei Meng
  • Qinghua Feng

Abstract

In this paper, an auxiliary equation method is introduced for seeking exact solutions expressed in variable coefficient function forms for fractional partial differential equations, where the concerned fractional derivative is defined by the conformable fractional derivative. By the use of certain fractional transformation, the fractional derivative in the equations can be converted into integer order case with respect to a new variable. As for applications, we apply this method to the time fractional two‐dimensional Boussinesq equation and the space‐time fractional (2+1)‐dimensional breaking soliton equation. As a result, some exact solutions including variable coefficient function solutions as well as solitary wave solutions for the two equations are found.

Suggested Citation

  • Fanwei Meng & Qinghua Feng, 2018. "Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:4596506
    DOI: 10.1155/2018/4596506
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    References listed on IDEAS

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    1. Fanwei Meng, 2013. "A New Approach for Solving Fractional Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, May.
    2. Fanwei Meng & Qinghua Feng, 2013. "A New Fractional Subequation Method and Its Applications for Space‐Time Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Fanwei Meng & Qinghua Feng, 2013. "A New Fractional Subequation Method and Its Applications for Space-Time Fractional Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, July.
    4. Fanwei Meng, 2013. "A New Approach for Solving Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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