An inverse problem for a generalized fractional diffusion

Khaled M. Furati; Olaniyi S. Iyiola; Mokhtar Kirane

doi:10.1016/j.amc.2014.10.046

An inverse problem for a generalized fractional diffusion

Khaled M. Furati, Olaniyi S. Iyiola, Mokhtar Kirane

Mathematics

King Fahd University for Petroleum and Minerals (KFUPM)

Research output: Contribution to journal › Article › peer-review

83 Scopus citations

Abstract

We propose a method for determining the solution and source term of a generalized time-fractional diffusion equation. The method is based on selecting a bi-orthogonal basis of ^L2 space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag-Leffler function is used to relax the smoothness requirement on these conditions.

Original language	British English
Pages (from-to)	24-31
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	249
DOIs	https://doi.org/10.1016/j.amc.2014.10.046
State	Published - 15 Dec 2014

Keywords

Anomalous diffusion
Bi-orthogonal system
Fractional derivative
Fractional diffusion equation
Inverse problem
Mittag-Leffler function

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10.1016/j.amc.2014.10.046

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title = "An inverse problem for a generalized fractional diffusion",

abstract = "We propose a method for determining the solution and source term of a generalized time-fractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L2 space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag-Leffler function is used to relax the smoothness requirement on these conditions.",

keywords = "Anomalous diffusion, Bi-orthogonal system, Fractional derivative, Fractional diffusion equation, Inverse problem, Mittag-Leffler function",

author = "Furati, {Khaled M.} and Iyiola, {Olaniyi S.} and Mokhtar Kirane",

note = "Funding Information: The authors are grateful for the support provided by King Fahd University of Petroleum and Minerals through Project No. FT121003. Publisher Copyright: {\textcopyright} 2014 Elsevier Inc. All rights reserved.",

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AU - Furati, Khaled M.

AU - Iyiola, Olaniyi S.

AU - Kirane, Mokhtar

N1 - Funding Information: The authors are grateful for the support provided by King Fahd University of Petroleum and Minerals through Project No. FT121003. Publisher Copyright: © 2014 Elsevier Inc. All rights reserved.

PY - 2014/12/15

Y1 - 2014/12/15

N2 - We propose a method for determining the solution and source term of a generalized time-fractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L2 space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag-Leffler function is used to relax the smoothness requirement on these conditions.

AB - We propose a method for determining the solution and source term of a generalized time-fractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L2 space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag-Leffler function is used to relax the smoothness requirement on these conditions.

KW - Anomalous diffusion

KW - Bi-orthogonal system

KW - Fractional derivative

KW - Fractional diffusion equation

KW - Inverse problem

KW - Mittag-Leffler function

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U2 - 10.1016/j.amc.2014.10.046

DO - 10.1016/j.amc.2014.10.046

M3 - Article

AN - SCOPUS:84911366140

SN - 0096-3003

VL - 249

SP - 24

EP - 31

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

An inverse problem for a generalized fractional diffusion

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Keywords

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