Statistical convergence of new type difference sequences with Caputo fractional derivative

Abstract

In this study, we discuss the idea of difference operators $ \Delta _{p}^{\alpha }, \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 $ \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.

Keywords

• difference operators
• statistical convergence
• sequence spaces
• fractional difference operators