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Existence and uniqueness results and analytical solution of the multi-dimensional Riesz space distributed-order advection–diffusion equation via two-step Adomian decomposition method

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Abstract

In this article, we introduced for the first time the two-step Adomian decomposition method (TSADM) for solving the multi-dimensional Riesz space distributed-order advection–diffusion (RSDOAD) equation. The TSADM was successfully applied to obtain the analytical solution of the multi-dimensional (RSDOAD) equation. The analytical solution has been obtained without approximation/discretization of the Riesz fractional operator. Furthermore, new results for the existence are obtained with the help of some fixed point theorems, while the uniqueness of the solution was investigated employing the Banach contraction principle. Finally, we included a generalized example to demonstrate the validity and application of the proposed method. The obtained results conclude that the proposed method is powerful and efficient for the considered problem compared to the other existing methods.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh, 211004, India

    Pratibha Verma & Manoj Kumar

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  1. Pratibha Verma
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  2. Manoj Kumar
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Correspondence to Manoj Kumar.

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Verma, P., Kumar, M. Existence and uniqueness results and analytical solution of the multi-dimensional Riesz space distributed-order advection–diffusion equation via two-step Adomian decomposition method. Engineering with Computers 38, 2051–2066 (2022). https://doi.org/10.1007/s00366-020-01194-6

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