Series Solutions to a Class of Initial Value Problems with Space-Fractional Derivatives

Authors

  • Songabsorn Manorod
  • Duangkamol Poltem
  • Araya Wiwatwanich Department of Mathematics, Faculty of Science, Burapha University

Keywords:

Partial Caputo Derivative, Fractional Differential Equations

Abstract

In this paper, we propose a semi-analytic method to provide Taylor series solutions to the initial value problems of space-fractional differential equations in the form

 

 

where is any linear operator of finite arguments and . Some examples have been demonstrated by using the technique of the proposed method.

 

Author Biography

  • Araya Wiwatwanich, Department of Mathematics, Faculty of Science, Burapha University
    Department of Mathematics, Faculty of Science, Burapha University, Chonburi

References

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Aghili A, Motahhari A, “Integral transform method for solving non homogenous time fractional partial differential equationsâ€, Differential Equations and Control Processes, no. 4, pp.194-204, 2011.

Das S, “Analytic solution of a fractional diffusion equation by variational iteration methodâ€, Computers and Mathematics with Applications, vol. 57, pp.483-487, 2009.

Cheng J. F, Chu Y. M, “Solution to the linear fractional differential equation using Adomian Decomposition Methodâ€, Mathematics Problems in Engineering, pp.1-14, 2011.

Kutafina E, “Taylor series for Adomian decomposition methodâ€, vol. 88, no. 17, pp.3677-3684, 2011.

Das S, Functional Fractional Calculus, 2nd ed., Springer-Verlag, Berlin, Heldelbery, 2011.

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Published

2016-08-15

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Section

Articles

How to Cite

Series Solutions to a Class of Initial Value Problems with Space-Fractional Derivatives. (2016). Asian Journal of Applied Sciences, 4(4). https://ajouronline.com/index.php/AJAS/article/view/3977

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