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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.17538 |
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Table of Contents:
- This paper intends to develop a $q$-difference operator $\nabla^{(γ)}_q$ of fractional order $γ$, and give several intriguing properties of this new difference operator. Our main focus remains on the construction of sequence spaces $\ell_p(\nabla^{(γ)})$ and $\ell_\infty (\nabla^{(γ)})$, at the same time comparing these spaces with those already exist in the literature. Apart from obtaining Schauder basis, we determine $α$-, $β$-, and $γ$-duals of the newly defined spaces. A section is also devoted for characterizing matrix classes $(\ell_p(\nabla^{(γ)}),\mathfrak X),$ where $\mathfrak X$ is any of the spaces $\ell_\infty,$ $c,$ $c_0$ and $\ell_1$.