In this study, we discuss the idea of difference operators ${\mathrm{\Delta }}_p^{\alpha },{\mathrm{\Delta }}_p^{\left(\alpha \right)}$ $\left(\alpha \in \mathbb{R}\right)$ and examine some properties of these operators. We also describe the concepts of ordered statistical convergence and lacunary statistical by using the ${\mathrm{\Delta }}_p^{\alpha }$-difference operator. We examine some features of these sequence spaces and present some inclusion theorems. We obtain the Caputo fractional derivative in this work.