Gegenbauer Cardinal Functions for the Inverse Source Parabolic Problem with a Time-Fractional Diffusion Equation

In this paper, we study a time-fractional inverse source problem. We introduce a new variable and transform inverse problem to an equivalent direct problem. By using maximum principle approach, the existence, uniqueness and stability of the inverse problem are displayed, then a numerical method is p...

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Bibliographic Details
Published inJournal of computational and theoretical transport Vol. 46; no. 5; pp. 307 - 329
Main Authors Rostamy, D., Abdollahi, N.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 29.07.2017
Taylor & Francis Ltd
Subjects
Cardinal function
fractional derivative
Gegenbauer polynomials
Inverse problems
inverse source problem
Mathematical analysis
Maximum principle
Numerical analysis
Uniqueness
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Summary:In this paper, we study a time-fractional inverse source problem. We introduce a new variable and transform inverse problem to an equivalent direct problem. By using maximum principle approach, the existence, uniqueness and stability of the inverse problem are displayed, then a numerical method is proposed to solve the problem. The main idea of the proposed method is based on expanding the approximate solution as the elements of Gegenbauer cardinal function. By using derivative and fractional derivative matrixes, the problem is reduced to the solution of a system of algebraic equations thus greatly simplifying the problem. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes.
ISSN:2332-4309
2332-4325
DOI:10.1080/23324309.2017.1352514