MATEMATIČKI VESNIK МАТЕМАТИЧКИ ВЕСНИК

 FRACTIONAL INTEGRAL INEQUALITIES OF VARIABLE ORDER ON SPHERICAL SHELL G. A. Anastassiou AbstractHere 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

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