Inverse problems for fractional partial differential equations

Author(s)

• Kaltenbacher, Barbara
• Rundell, William

Bibliographic Information

Inverse problems for fractional partial differential equations

Barbara Kaltenbacher, William Rundell

（Graduate studies in mathematics, 230）

American Mathematical Society, c2023

• : paperback

Note

Includes bibliographical references (p. 483-502) and index

Description and Table of Contents

Description

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.

Table of Contents

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 Bibliography Index

by "Nielsen BookData"

Details

• NCID: BD05455455
• ISBN:
  • 9781470472771
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xiii, 505 p.
• Size: 26 cm
• Classification:
  • LCC : QA378.5
• Subject Headings:
  • LCSH : Inverse problems (Differential equations) -- Textbooks
  • LCSH : Fractional differential equations -- Textbooks
• Parent Bibliography ID:
  • BA20542214