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An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

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  • M. Bishehniasar
  • S. Salahshour
  • A. Ahmadian
  • F. Ismail
  • D. Baleanu

Abstract

The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems.

Suggested Citation

  • M. Bishehniasar & S. Salahshour & A. Ahmadian & F. Ismail & D. Baleanu, 2017. "An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations," Complexity, Hindawi, vol. 2017, pages 1-12, December.
    • Handle: RePEc:hin:complx:8718209
    DOI: 10.1155/2017/8718209
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    References listed on IDEAS

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    1. Yu, Bo & Jiang, Xiaoyun & Wang, Chu, 2016. "Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 106-118.
    2. Ahmadian, A. & Salahshour, S. & Ali-Akbari, M. & Ismail, F. & Baleanu, D., 2017. "A novel approach to approximate fractional derivative with uncertain conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 68-76.
    3. Yang, Xiao-Jun & Tenreiro Machado, J.A. & Srivastava, H.M., 2016. "A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 143-151.
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