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A new Sumudu transform iterative method for time-fractional Cauchy reaction-diffusion equation.

Kangle Wang1, Sanyang Liu1

  • 1School of Mathematics and Statistics, Xidian University, Xi'an, 710118 China.

Springerplus
|July 8, 2016
PubMed
Summary

A new Sumudu transform iterative method offers a simple and efficient way to find approximate analytical solutions for time-fractional Cauchy reaction-diffusion equations.

Keywords:
Caputo fractional derivativeDiffusion equationSumudu transform

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Area of Science:

  • Applied Mathematics
  • Numerical Analysis
  • Fractional Calculus

Background:

  • Fractional differential equations (FDEs) are increasingly used to model complex phenomena.
  • Cauchy reaction-diffusion equations with time-fractional derivatives present significant analytical challenges.

Purpose of the Study:

  • To introduce and validate a novel iterative method for solving time-fractional Cauchy reaction-diffusion equations.
  • To demonstrate the simplicity and efficiency of the proposed numerical technique.

Main Methods:

  • Development of a new iterative method based on the Sumudu transform.
  • Application of the Sumudu transform iterative method to time-fractional Cauchy reaction-diffusion equations.
  • Numerical verification of the method's performance.

Main Results:

  • The Sumudu transform iterative method successfully provides approximate analytical solutions.
  • The proposed method is shown to be easy to implement and understand.
  • Numerical results confirm the method's simplicity and high efficiency.

Conclusions:

  • The established Sumudu transform iterative method is a powerful tool for addressing time-fractional Cauchy reaction-diffusion equations.
  • This approach offers a practical and effective alternative for researchers and practitioners in applied mathematics and related fields.