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We generalized the concepts in probability of rough lacunary statistical by introducing the diference operator of fractional order, where is a proper fraction and = (mnk ) is anyxed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related triple diference sequence spaces. The main focus of the present paper is todoi:10.5269/bspm.v37i1.32155 fatcat:ay7wivct5ncxlmrxmjz3xrmuce