This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.

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a b s t r a c tIn this paper, we study the determinant of perturbation connected with the dissipative operator L generated in L 2 (I) by (1.1)-(1.5). Then using Livšic's theorem, we investigate the problem of completeness of the system of eigenfunctions and associated functions of L.