Identities on fractional integrals and various integral transforms
Copyright policy )Identities on fractional integrals and various integral transforms
There is an important property relating the Laplace transform to integration, \(L\{\frac{f(t)}{t}\}=\int^\infty_sF(x)dx\). The author extends this identity to Weyl's fractional integration. In this spirit, he provides several interesting theorems relating the Weyl fractional integral and the Riemann-Liouville fractional integral to some classical integral transforms -- the Laplace, Stieltjes, Hankel, Widder potential transforms and the \(K\)-transform. As application, some interesting infinite integrals are evaluated involving elementary and special functions.
- Ithaca College United States
Exponential integral function, Weyl fractional integral, fractional derivatives, Laplace transform, complementary error function, Complementary error function, Generalized Stieltjes transform, Error function, Fractional derivatives and integrals, K-transform, Hankel transform, Widder potential transform, modified Bessel functions of the third kind, Fractional derivatives, Modified Bessel functions of the third kind, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), Parseval-Goldstein type of identities, exponential integral function, Bessel functions, generalized Stieltjes transform, Stieltjes transform, \(K\)-transform, Special integral transforms (Legendre, Hilbert, etc.), Bessel and Airy functions, cylinder functions, \({}_0F_1\), Riemann-Liouville fractional integral, error function
Exponential integral function, Weyl fractional integral, fractional derivatives, Laplace transform, complementary error function, Complementary error function, Generalized Stieltjes transform, Error function, Fractional derivatives and integrals, K-transform, Hankel transform, Widder potential transform, modified Bessel functions of the third kind, Fractional derivatives, Modified Bessel functions of the third kind, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), Parseval-Goldstein type of identities, exponential integral function, Bessel functions, generalized Stieltjes transform, Stieltjes transform, \(K\)-transform, Special integral transforms (Legendre, Hilbert, etc.), Bessel and Airy functions, cylinder functions, \({}_0F_1\), Riemann-Liouville fractional integral, error function
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