In this article, we introduce the new sequence spaces \(w(\mathbb {E}_1,\Delta ^{(\psi )},f)_c,\) \(w(\mathbb {E}_1,\Delta ^{(\psi )},f)_{c_{0}}\) and \(w(\mathbb {E}_1,\Delta ^{(\psi )},f)_{\ell _\infty }\) , defined by an operator that combines the Euler-Riesz transformation with a fractional difference operator, applied through a modulus function. These spaces are constructed within the framework of fractional order \((\psi )\) , extending classical sequence space theory. We explore their fundamental topological properties, including completeness and the existence of a Schauder basis. Additionally, we characterize their \(\alpha \) -, \(\beta \) - and \(\gamma \) -duals, providing insights into their functional structure.
