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 | English |
|---|---|
| Pages (from-to) | 24-31 |
| Number of pages | 8 |
| Journal | Applied Mathematics and Computation |
| Volume | 249 |
| DOIs | |
| State | Published - 15 Dec 2014 |
Bibliographical note
Publisher Copyright:© 2014 Elsevier Inc. All rights reserved.
Keywords
- Anomalous diffusion
- Bi-orthogonal system
- Fractional derivative
- Fractional diffusion equation
- Inverse problem
- Mittag-Leffler function
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
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