FRACTIONAL INTEGRAL INEQUALITIES OF VARIABLE ORDER ON SPHERICAL SHELL


G. A. Anastassiou




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.