Softcover ISBN:  9781470472771 
Product Code:  GSM/230.S 
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AMS Member Price:  $71.20 
eBook ISBN:  9781470472764 
Product Code:  GSM/230.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470472771 
eBook: ISBN:  9781470472764 
Product Code:  GSM/230.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 
Softcover ISBN:  9781470472771 
Product Code:  GSM/230.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470472764 
Product Code:  GSM/230.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470472771 
eBook ISBN:  9781470472764 
Product Code:  GSM/230.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 230; 2023; 505 ppMSC: 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.
ReadershipGraduate students and researchers interested in Partial Differential Equations.

Table of Contents

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


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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.
Graduate students and researchers interested in Partial Differential Equations.

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