We introduce Ces \(\grave{a}\) ro sequence space \(\text {Ces}(\Delta ^{(\alpha ;l)},\mathcal {F},p)\) defined by the l-fractional difference operator \(\Delta ^{(\alpha ;l)}\) and sequence of modulus functions \(\mathcal {F}=(f_{n})\) , where \(p=(p_{n})\) is a bounded sequence of positive real numbers, and \(\alpha \) and l are real numbers. \(\text {Ces}(\Delta ^{(\alpha ;l)},\mathcal {F},p)\) generalises the existing Ces \(\grave{a}\) ro sequence spaces introduced by earlier authors. In this paper, we proved that \(\text {Ces}(\Delta ^{(\alpha ;l)},\mathcal {F},p)\) is complete paranormed space. Various inclusion relations are also obtained for this sequence space by taking two different sequences of modulus functions or two different bounded sequences of positive real numbers. In the last section, we determined inclusion relations for the sequence space \(\text {Ces}(\Delta ^{(\alpha ;l)},f^{\nu },p)\) , where \(f^{\nu }\) means \(f\circ f\circ \cdots \circ f \) ( \(\nu \) times).
