Karakas, Abdulkadir2024-12-242024-12-2420222473-6988https://doi.org/10.3934/math.2022940https://hdl.handle.net/20.500.12604/8393In this study, we discuss the idea of di fference operators Delta(a)(p), Delta((a))(p) (alpha is an element of R) and examine some properties of these operators. We also describe the concepts of ordered statistical convergence and lacunary statistical by using the Delta(a)(p)-difference operator. We examine some features of these sequence spaces and present some inclusion theorems. We obtain the Caputo fractional derivative in this work.eninfo:eu-repo/semantics/openAccessdifference operatorsstatistical convergencesequence spacesfractional difference operatorsArticle791709117104Q1WOS:000855360400011Q12-s2.0-8513457349810.3934/math.2022940