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The Solution of Initial Boundary Value Problem with Time and Space-Fractional Diffusion Equation via a Novel Inner Product
Joint Authors
Kodal Sevindir, Hulya
Demir, Ali
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-06
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
The main goal of this study is to find the solution of initial boundary value problem for the one-dimensional time and space-fractional diffusion equation which is a very intriguing topic for many researchers.
With the aim of newly defined inner product, which is the main contribution of this study, the analytic solution of the boundary value problem is obtained.
The time and space-fractional derivatives are defined in the Caputo sense which is more suitable than Riemann-Liouville sense.
We apply the separation of variables method to reduce the problem to two separate fractional ODEs.
The generalized solution is constructed/formed in the form of a Fourier series with respect to the eigenfunctions of a certain eigenvalue problem.
In order to obtain the coefficients of the Fourier series for the solution, we define a new inner product which is the key point of study.
American Psychological Association (APA)
Kodal Sevindir, Hulya& Demir, Ali. 2018. The Solution of Initial Boundary Value Problem with Time and Space-Fractional Diffusion Equation via a Novel Inner Product. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-6.
https://search.emarefa.net/detail/BIM-1119070
Modern Language Association (MLA)
Kodal Sevindir, Hulya& Demir, Ali. The Solution of Initial Boundary Value Problem with Time and Space-Fractional Diffusion Equation via a Novel Inner Product. Advances in Mathematical Physics No. 2018 (2018), pp.1-6.
https://search.emarefa.net/detail/BIM-1119070
American Medical Association (AMA)
Kodal Sevindir, Hulya& Demir, Ali. The Solution of Initial Boundary Value Problem with Time and Space-Fractional Diffusion Equation via a Novel Inner Product. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-6.
https://search.emarefa.net/detail/BIM-1119070
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119070