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Numerical Methods for Fractional Calculus presents numerical
methods for fractional integrals and fractional derivatives, finite
difference methods for fractional ordinary differential equations
(FODEs) and fractional partial differential equations (FPDEs), and
finite element methods for FPDEs. The book introduces the basic
definitions and properties of fractional integrals and derivatives
before covering numerical methods for fractional integrals and
derivatives. It then discusses finite difference methods for both
FODEs and FPDEs, including the Euler and linear multistep methods.
The final chapter shows how to solve FPDEs by using the finite
element method. This book provides efficient and reliable numerical
methods for solving fractional calculus problems. It offers a
primer for readers to further develop cutting-edge research in
numerical fractional calculus. MATLAB (R) functions are available
on the book's CRC Press web page.
Numerical Methods for Fractional Calculus presents numerical
methods for fractional integrals and fractional derivatives, finite
difference methods for fractional ordinary differential equations
(FODEs) and fractional partial differential equations (FPDEs), and
finite element methods for FPDEs. The book introduces the basic
definitions and properties of fractional integrals and derivatives
before covering numerical methods for fractional integrals and
derivatives. It then discusses finite difference methods for both
FODEs and FPDEs, including the Euler and linear multistep methods.
The final chapter shows how to solve FPDEs by using the finite
element method. This book provides efficient and reliable numerical
methods for solving fractional calculus problems. It offers a
primer for readers to further develop cutting-edge research in
numerical fractional calculus. MATLAB (R) functions are available
on the book's CRC Press web page.
Due to its ubiquity across a variety of fields in science and
engineering, fractional calculus has gained momentum in industry
and academia. While a number of books and papers introduce either
fractional calculus or numerical approximations, no current
literature provides a comprehensive collection of both topics. This
monograph introduces fundamental information on fractional calculus
and provides a detailed treatment of existing numerical
approximations. Theory and Numerical Approximations of Fractional
Integrals and Derivatives presents an inclusive review of
fractional calculus in terms of theory and numerical methods and
systematically examines almost all existing numerical
approximations for fractional integrals and derivatives. The
authors consider the relationship between the fractional Laplacian
and the Riesz derivative, a key component absent from other related
texts, and highlight recent developments, including their own
research and results. The book's core audience spans several
fractional communities, including those interested in fractional
partial differential equations, the fractional Laplacian, and
applied and computational mathematics. Advanced undergraduate and
graduate students will find the material suitable as a primary or
supplementary resource for their studies.
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