Title:
FRACTIONAL_DIFFERINTEGRAL
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Description: Description
The n-th order derivative or integral of a function defined in a given
range [a,b] is calculated through Fourier series expansion, where n is
any real number and not necessarily integer. The necessary integrations
are performed with the Gauss-Legendre quadrature rule. Selection for the
number of desired Fourier coefficient pairs is made as well as for the
number of the Gauss-Legendre integration points.
Unlike many publicly available functions, the Gauss integration points k
can be calculated for k>=46. The algorithm does not rely on the build-in
Matlab routine roots to determine the roots of the Legendre polynomial,
but finds the roots by looking for the eigenvalues of an alternative
version of the companion matrix of the k th degree Legendre polynomial.
The companion matrix is constructed as a symmetrical matrix, guaranteeing
that all the eigenvalues (roots) will be real. On the contrary, the
roots function us
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File list (Check if you may need any files):
FRACTIONAL_DIFFERINTEGRAL\cubic_polynomial_differintegral.m
.........................\fourier.m
.........................\fourier_diffint.m
.........................\html\cubic_polynomial_differintegral.html
.........................\....\cubic_polynomial_differintegral.png
.........................\....\cubic_polynomial_differintegral_01.png
.........................\....\cubic_polynomial_differintegral_02.png
.........................\....\cubic_polynomial_differintegral_03.png
.........................\....\cubic_polynomial_differintegral_eq33319.png
.........................\....\cubic_polynomial_differintegral_eq43362.png
.........................\....\cubic_polynomial_differintegral_eq45880.png
.........................\....\cubic_polynomial_differintegral_eq47863.png
.........................\....\cubic_polynomial_differintegral_eq62195.png
.........................\....\cubic_polynomial_differintegral_eq66619.png
.........................\....\cubic_polynomial_differintegral_eq71312.png
.........................\....\cubic_polynomial_differintegral_eq76742.png
.........................\....\cubic_polynomial_differintegral_eq83100.png
.........................\....\cubic_polynomial_differintegral_eq85163.png
.........................\....\cubic_polynomial_differintegral_eq86385.png
.........................\....\cubic_polynomial_differintegral_eq90533.png
.........................\....\cubic_polynomial_differintegral_eq91427.png
.........................\....\cubic_polynomial_differintegral_eq92095.png
.........................\....\cubic_polynomial_differintegral_eq95823.png
.........................\....\cubic_polynomial_differintegral_eq99834.png
.........................\....\identity_function_differintegral.html
.........................\....\identity_function_differintegral.png
.........................\....\identity_function_differintegral_01.png
.........................\....\identity_function_differintegral_02.png
.........................\....\identity_function_differintegral_eq33319.png
.........................\....\identity_function_differintegral_eq43362.png
.........................\....\identity_function_differintegral_eq45880.png
.........................\....\identity_function_differintegral_eq47863.png
.........................\....\identity_function_differintegral_eq62195.png
.........................\....\identity_function_differintegral_eq66619.png
.........................\....\identity_function_differintegral_eq71312.png
.........................\....\identity_function_differintegral_eq76742.png
.........................\....\identity_function_differintegral_eq83100.png
.........................\....\identity_function_differintegral_eq85163.png
.........................\....\identity_function_differintegral_eq86385.png
.........................\....\identity_function_differintegral_eq90533.png
.........................\....\identity_function_differintegral_eq91427.png
.........................\....\identity_function_differintegral_eq92095.png
.........................\....\identity_function_differintegral_eq95823.png
.........................\....\identity_function_differintegral_eq99834.png
.........................\....\tabular_function_differintegral.html
.........................\....\tabular_function_differintegral.png
.........................\....\tabular_function_differintegral_01.png
.........................\....\tabular_function_differintegral_02.png
.........................\....\tabular_function_differintegral_03.png
.........................\....\tabular_function_differintegral_eq33319.png
.........................\....\tabular_function_differintegral_eq43362.png
.........................\....\tabular_function_differintegral_eq45880.png
.........................\....\tabular_function_differintegral_eq47863.png
.........................\....\tabular_function_differintegral_eq62195.png
.........................\....\tabular_function_differintegral_eq66619.png
.........................\....\tabular_function_differintegral_eq71312.png
.........................\....\tabular_fun
