Generalized fractional integral transform with Whittaker's kernel

M. Manuela  Rodrigues

doi:10.1063/1.4827228

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Published Online: 13 November 2013

Generalized fractional integral transform with Whittaker's kernel

AIP Conference Proceedings 1561, 194 (2013); https://doi.org/10.1063/1.4827228

M. Manuela Rodrigues

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ABSTRACT

In this work we present two generalizations (see the operators

I_{0+}^{α,ρ,σ}

and

I_{-}^{α,ρ,σ}

defined below) of the classical Liouville fractional integrals. We study their boundedness as operators mapping the space L_v,_r into the spaces

L_{v+2+ \frac{Re (α)}{2} −2 Re (ρ),r}

and

L_{v+1+− Re (ρ),r}

. In the end, we will apply our generalization to some particular functions.

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