Fractional integrals and derivatives : theory and applications
著者
書誌事項
Fractional integrals and derivatives : theory and applications
Gordon and Breach Science Publishers, c1993
- タイトル別名
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Интегралы и производные дробного порядка и некоторые их приложения
Integraly i proizvodnye drobnogo pori︠a︡dka i nekotorye ikh prilozhenii︠a︡
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注記
Includes bibliographical references (p. [873]-951) and index
内容説明・目次
内容説明
This monograph is devoted to the systematic and comprehensive exposition of classical and modern results in the theory of fractional integrals and their applications. Various aspects of this theory, such as functions of one and several variables, periodical and non-periodical cases, and the technique of hypersingular integrals are studied. All existing types of fractional integro-differentiation are examined and compared. The applications of fractional calculus to first order integral equations with power and power logarithmic kernels, and with special functions in kernels and to Euler-Poisson-Darboux's type equations and differential equations of fractional order are discussed. The text should be of use not only to graduates and postgraduates of mathematical physics and engineering, but also to specialists in the field.
目次
- Fractional integrals and derivatives on an interval
- fractional integrals and derivatives on the real axis and half-axis
- further properties of fractional integrals and derivatives
- other forms of fractional integrals and derivatives
- fractional integrodifferentiation of functions of many variables
- applications to integral equations of the first kind with power and power-logarithmic kernels
- integral equations fo the first kind with special function kernels
- applications to differential equations.
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