# Inverse problems for fractional partial differential equations / Barbara Kaltenbacher, William Rundell.

Material type: TextLanguage: English Series: Graduate studies in mathematics ; volume 230Publication details: American Mathematical Society, 2020.Description: pages cmISBN:- 9781470472450
- 9781470472771

- Inverse problems (Differential equations)
- Fractional differential equations
- Partial differential equations -- Miscellaneous topics -- Inverse problems
- Partial differential equations -- Miscellaneous topics -- Fractional partial differential equations
- Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Inverse problems
- Real functions -- Functions of one variable -- Fractional derivatives and integrals
- Partial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations
- Partial differential equations -- Equations of mathematical physics and other areas of application
- Partial differential equations -- Miscellaneous topics -- Improperly posed problems
- Operator theory -- Partial differential operators -- Partial differential operators
- Numerical analysis -- Numerical analysis in abstract spaces -- Improperly posed problems; regularization
- -- Textbooks
- -- Textbooks
- Mathematics

- 515.353 23/eng20230111 KAL

- 35R30 | 35R11 | 65M32 | 26A33 | 35K57 | 35Qxx | 35R25 | 47F05 | 65J20

Item type | Current library | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|

Project book | CUTN Central Library Sciences | Non-fiction | 515.353 KAL (Browse shelf(Opens below)) | Checked out to Renuka Devi V (20019T) | 31/01/2024 | 48913 |

Includes bibliographical references and index.

Chapters

Preamble

Genesis of fractional models

Special functions and tools

Fractional calculus

Fractional ordinary differential equations

Mathematical theory of subdiffusion

Analysis of fractionally damped wave equations

Methods for solving inverse problems

Fundamental inverse problems for fractional order models

Inverse problems for fractional diffusion

Inverse problems for fractionally damped wave equations

Outlook beyond Abel

Mathematical preliminaries

Volume: 230; 2023; 505 pp

MSC: Primary 35; 65; Secondary 26; 47; 60;

As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters.

The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case.

The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.

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