COMPOSITIONS OF FRACTIONAL INTEGRALS AND DERIVATIVES WITH BESSEL TYPEFUNCTION AND SOLUTION OF DIFFERENTIAL AND INTEGRAL-EQUATIONS

The compositional relations. of Liouville fractional integrals grid de rivatives with the special function of Bessel type generalizing modifi ed Bessel function of the third kind are proved. It is shown that such a special function is invariant with respect to certain generalized f ractional differentiation operators, in particular with respect to Bes sel-Clifford differential operator and differential operator of axisym metric potential theory.Applications are given to obtain explicit solu tions of differential equations of fractional and integer order and of Volterra integral equations of the third kind.