FRACTIONAL INTEGRAL INEQUALITIES OF VARIABLE ORDER ON SPHERICAL SHELL

Abstract

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