Adomian decomposition method for time fractional diffusion-reaction equation | ||
| Delta Journal of Science | ||
| Volume 51, Issue 1, July 2025, Pages 130-140 PDF (951.32 K) | ||
| Document Type: Research and Reference | ||
| Authors | ||
| Ali Mohammadein* 1; Mohamed El-Amin1; Emad Abo-Eldahab2; Hegagi Ali1 | ||
| 1Mathematics Department, Faculty of Science, Aswan University, Aswan 81528, Egypt | ||
| 2Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt | ||
| Abstract | ||
| In this paper, the Adomian decomposition method (ADM) and specially its symbolic capability on the usage for determination of a solution to partial differential equations is explored. The Adomian decomposition method is used to solve the time fractional diffusion-reaction equation. This method is applied for two models of the time fractional diffusion-reaction equations (Autocatalytic reaction and Bistable and Schlogl models). The results given by this method show that, the effectiveness of the solution is closed Adomian decomposition method for time fractional diffusion-reaction equation to practical proposals of our research and is close to the exact solution. Moreover, the current method is introduced for the solution of the time fractional diffusion-reaction equation. The concentration of the species function is proportional directly with all the physical parameters in the “Bistable or Schlogl model” and inversely in case of” Autocatalytic model” respectively. The approximate solution considered that, the first and second driven terms of the decomposition are enough for the approximate solution. | ||
| Keywords | ||
| Adomian decomposition method; Adomian polynomials; diffusion-reaction equation; Fractional differential equations; Autocatalytic reaction and Bistable or Schlogl models Solution | ||
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