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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Computation of solution to fractional order partial reaction diffusion equations.

Haji Gul1, Hussam Alrabaiah2,3, Sajjad Ali4

  • 1Department of Mathematics, Abdul Wali Khan Univeristy, Mardan, Pakistan.

Journal of Advanced Research
|September 14, 2020
PubMed
Summary

This study introduces a novel hybrid method combining Laplace transform and Adomian decomposition to solve fractional reaction-diffusion equations, crucial for modeling spatial effects in various scientific fields.

Keywords:
35A2235A2535K57Caputo operatorDecomposition techniqueFractional order CRDELADM

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Area of Science:

  • Applied Mathematics
  • Mathematical Modeling
  • Numerical Analysis

Background:

  • Fractional reaction-diffusion equations are essential for modeling complex phenomena in engineering, biology, and ecology.
  • Solving these equations, especially nonlinear ones, presents significant analytical and computational challenges.

Purpose of the Study:

  • To develop and present an efficient hybrid analytical method for solving fractional-order Cauchy reaction-diffusion equations.
  • To demonstrate the applicability of the proposed method to both linear and nonlinear problems.

Main Methods:

  • A hybrid approach integrating the Laplace transform with the Adomian decomposition method was employed.
  • The fractional derivative was considered in the Caputo sense.
  • MATLAB was utilized for computational purposes.

Main Results:

  • The proposed hybrid method successfully provided series-form analytical solutions for the fractional reaction-diffusion equations.
  • The obtained approximate solutions exhibited rapid convergence towards the exact solutions.
  • The method proved effective for handling both linear and nonlinear reaction-diffusion problems.

Conclusions:

  • The coupled Laplace transform and Adomian decomposition method offers an efficient and accurate technique for solving fractional reaction-diffusion equations.
  • This approach provides a valuable tool for researchers modeling spatial effects in diverse scientific disciplines with reduced computational cost.