This paper presents the Elzaki homotopy perturbation transform scheme ($ {\bf{E}} $HPTS) to analyze the approximate solution of the multi-dimensional fractional diffusion equation. The Atangana-Baleanu derivative is considered in the Caputo sense. First, we apply Elzaki transform ($ {\bf{E}} $T) to obtain a recurrence relation without any assumption or restrictive variable. Then, this relation becomes very easy to handle for the implementation of the homotopy perturbation scheme (HPS). We observe that HPS produces the iterations in the form of convergence series that approaches the precise solution. We provide the graphical representation in 2D plot distribution and 3D surface solution. The error analysis shows that the solution derived by $ {\bf{E}} $HPTS is very close to the exact solution. The obtained series shows that $ {\bf{E}} $HPTS is a very simple, straightforward, and efficient tool for other problems of fractional derivatives.
Citation: Muhammad Nadeem, Ji-Huan He, Hamid. M. Sedighi. Numerical analysis of multi-dimensional time-fractional diffusion problems under the Atangana-Baleanu Caputo derivative[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8190-8207. doi: 10.3934/mbe.2023356
This paper presents the Elzaki homotopy perturbation transform scheme ($ {\bf{E}} $HPTS) to analyze the approximate solution of the multi-dimensional fractional diffusion equation. The Atangana-Baleanu derivative is considered in the Caputo sense. First, we apply Elzaki transform ($ {\bf{E}} $T) to obtain a recurrence relation without any assumption or restrictive variable. Then, this relation becomes very easy to handle for the implementation of the homotopy perturbation scheme (HPS). We observe that HPS produces the iterations in the form of convergence series that approaches the precise solution. We provide the graphical representation in 2D plot distribution and 3D surface solution. The error analysis shows that the solution derived by $ {\bf{E}} $HPTS is very close to the exact solution. The obtained series shows that $ {\bf{E}} $HPTS is a very simple, straightforward, and efficient tool for other problems of fractional derivatives.
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Muhammad Nadeem, Ji-Huan He, Hamid. M. Sedighi. Numerical analysis of multi-dimensional time-fractional diffusion problems under the Atangana-Baleanu Caputo derivative[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8190-8207. doi: 10.3934/mbe.2023356
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