A Fractional Finite Difference Method for Solving the Fractional Poisson Equation Based on the Shifted Grünwald Estimate

Authors

  • Abdollah BORHANIFAR Department of Mathematics, University of Mohaghegh Ardabili, Ardabil 56199-11367
  • Sohrab VALIZADEH Department of Mathematics, University of Mohaghegh Ardabili, Ardabil 56199-11367

Keywords:

Fractional Poisson equation, Riemann-Liouville fractional derivative, Shifted Grünwald Estimate, Taylor’s expansion of fractional order

Abstract

In this study a fractional Poisson equation is scrutinized through finite difference using the shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of the solution for the fractional Poisson equation is proved. Exact and numerical solutions are constructed and compared. Then numerical results show the efficiency of the proposed method.

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Author Biographies

Abdollah BORHANIFAR, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil 56199-11367

Departmnt of Mathematics

Sohrab VALIZADEH, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil 56199-11367

Departmnt of Mathematics

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Published

2013-07-03

How to Cite

BORHANIFAR, A., & VALIZADEH, S. (2013). A Fractional Finite Difference Method for Solving the Fractional Poisson Equation Based on the Shifted Grünwald Estimate. Walailak Journal of Science and Technology (WJST), 10(5), 427–435. Retrieved from https://wjst.wu.ac.th/index.php/wjst/article/view/280