On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by a Modulus Function

Let Γ(?) denotes the gamma function of a real number ? ∉ {0, −1, −2, … }. Then the difference matrix Δa of a fractional order ? is defined as Using the difference operator Δa , we introduce paranormed difference sequence spaces ?ఏ(Δఈ ?, Λ, ?) and ?ఏ(Δఈ, ?, Λ, ?) of fractional orders involving lacunary sequence, ?; modulus function, ? and multiplier sequence, Λ = (?). We investigate topological structures of these spaces and examine various inclusion relations.Keywords: Difference operator Δa , Paranormed sequence space, Lacunary sequence, Modulus function, Multiplier sequence.

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