Continuity with respect to fractional order of the time fractional diffusion-wave equation

Nguyen Huy Tuan; Donal O’Regan; Tran Bao Ngoc

doi:10.3934/eect.2020033

Continuity with respect to fractional order of the time fractional diffusion-wave equation

Nguyen Huy Tuan
, Donal O’Regan
, Tran Bao Ngoc

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

17 Citations (Scopus)

Abstract

This paper studies a time-fractional diffusion-wave equation with a linear source function. First, some stability results on parameters of the Mittag-Leffler functions are established. Then, we focus on studying the continuity of the solution of both the initial problem and the inverse initial value problems corresponding to the fractional-order in our main results. One of the difficulties encounteblack comes from estimating all constants independently of the fractional orders. Finally, we present some numerical results to confirm the effectiveness of our methods.

Original language	English
Pages (from-to)	773-793
Number of pages	21
Journal	Evolution Equations and Control Theory
Volume	9
Issue number	3
DOIs	https://doi.org/10.3934/eect.2020033
Publication status	Published - 1 Sep 2020

Keywords

Continuity/stability on fractional orders
Final value problem
Initial value problem
Inverse initial value problem
Time fractional wave equation

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Tuan, NH;O'Regan, D;Ngoc, TB

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10.3934/eect.2020033

Cite this

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abstract = "This paper studies a time-fractional diffusion-wave equation with a linear source function. First, some stability results on parameters of the Mittag-Leffler functions are established. Then, we focus on studying the continuity of the solution of both the initial problem and the inverse initial value problems corresponding to the fractional-order in our main results. One of the difficulties encounteblack comes from estimating all constants independently of the fractional orders. Finally, we present some numerical results to confirm the effectiveness of our methods.",

keywords = "Continuity/stability on fractional orders, Final value problem, Initial value problem, Inverse initial value problem, Time fractional wave equation",

author = "Tuan, \{Nguyen Huy\} and Donal O{\textquoteright}Regan and Ngoc, \{Tran Bao\}",

year = "2020",

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doi = "10.3934/eect.2020033",

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AU - Tuan, Nguyen Huy

AU - O’Regan, Donal

AU - Ngoc, Tran Bao

PY - 2020/9/1

Y1 - 2020/9/1

N2 - This paper studies a time-fractional diffusion-wave equation with a linear source function. First, some stability results on parameters of the Mittag-Leffler functions are established. Then, we focus on studying the continuity of the solution of both the initial problem and the inverse initial value problems corresponding to the fractional-order in our main results. One of the difficulties encounteblack comes from estimating all constants independently of the fractional orders. Finally, we present some numerical results to confirm the effectiveness of our methods.

AB - This paper studies a time-fractional diffusion-wave equation with a linear source function. First, some stability results on parameters of the Mittag-Leffler functions are established. Then, we focus on studying the continuity of the solution of both the initial problem and the inverse initial value problems corresponding to the fractional-order in our main results. One of the difficulties encounteblack comes from estimating all constants independently of the fractional orders. Finally, we present some numerical results to confirm the effectiveness of our methods.

KW - Continuity/stability on fractional orders

KW - Final value problem

KW - Initial value problem

KW - Inverse initial value problem

KW - Time fractional wave equation

UR - https://www.scopus.com/pages/publications/85090700159

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DO - 10.3934/eect.2020033

M3 - Article

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VL - 9

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EP - 793

JO - Evolution Equations and Control Theory

JF - Evolution Equations and Control Theory

IS - 3

ER -

Continuity with respect to fractional order of the time fractional diffusion-wave equation

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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