Abstract

Here left and right Riemann{-}Liouville generalized fractional radial integral operators of variable order over a spherical shell are introduced, as well as left and right weighted Caputo type generalized fractional radial derivatives of variable order over a spherical shell. After proving continuity of these operators, we establish a series of left and right fractional integral inequalities of variable order over the spherical shell of Opial and Hardy types. Extreme cases are met.

Keywords: Fractional Opial and Hardy type inequalities; generalized fractional operators of variable order; spherical shell.

MSC: 26A33, 26D10, 26D15

Pages:  42$-$55     

Volume  74 ,  Issue  1 ,  2022