Complex-Valued Symmetric Fractional Derivative on Time Scales

摘要

In this paper, we introduce the concept of symmetric fractional (noninteger order) derivative for functions defined on an arbitrary nonempty subset of real numbers (i.e., on a time scale), denoted by f~(◇~α) (t). Then the basic properties of this new operator are examined, and some related theorems are proved. We also give several examples.