NEW EXISTENCE, UNIQUENESS RESULTS FOR MULTI-DIMENSIONAL MULTI-TERM CAPUTO TIME-FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION ON CONVEX DOMAINS

Pratibha Verma; Manoj Kumar

doi:10.11948/20200217

2021 Volume 11 Issue 3

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Pratibha Verma, Manoj Kumar. NEW EXISTENCE, UNIQUENESS RESULTS FOR MULTI-DIMENSIONAL MULTI-TERM CAPUTO TIME-FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION ON CONVEX DOMAINS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1455-1480. doi: 10.11948/20200217

Citation:

Pratibha Verma, Manoj Kumar. NEW EXISTENCE, UNIQUENESS RESULTS FOR MULTI-DIMENSIONAL MULTI-TERM CAPUTO TIME-FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION ON CONVEX DOMAINS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1455-1480. doi: 10.11948/20200217

NEW EXISTENCE, UNIQUENESS RESULTS FOR MULTI-DIMENSIONAL MULTI-TERM CAPUTO TIME-FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION ON CONVEX DOMAINS

Pratibha Verma^1, ,,
Manoj Kumar¹

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

Corresponding author: Email: pratibhaverma@mnnit.ac.in (P. Verma)

Abstract

Abstract

In this paper, we investigate an efficient analytical method known as two step Adomian decomposition method (TSADM). This method does not require approximation/discretization, lengthy calculations and due to involvement of fractional operators and provides an exact solution. In this study, we generalize the multi-term time-fractional mixed sub-diffusion and diffusion-wave equation into multi dimensions with Caputo derivative for time fractional operators and obtain the exact solution. Furthermore, we establish the new results of existence and uniqueness of the solution using fixed point theory. To demonstrate the effectiveness of the proposed method, several generalized examples on the convex domain are considered.
- Fixed point theorems /
- Caputo's fractional operators /
- diffusionwave equation /
- two-step Adomian decomposition method
MSC: 47H10, 35R11

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References

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