On some generalisations of the Riemann-Liouville and Weyl fractional integrals and their applications

For functions f ∈ L Loc [0, ∞) the Riemann-Liouville operator of fractional integration I ∞ is defined by and its adjoint operator, the Weyl operator K α , is defined by for functions f ∈ L Loc [0, ∞) having a suitable behaviour at infinity.