Deformable derivative in complex domain

Abstract

In this article, we are proposing a limit-based definition, which we have termed as complex deformable derivative. The complex deformable derivative and complex deformable integral with non-integer order , coincides with the classical complex derivative for . The complex deformable derivative is defined by using a limit approach similar to the classical definition of derivative involving a parameter. This derivative is represented as the linear combination of the function and its integer-order derivative. We investigate the elementary properties of deformable derivative and integral. The results have been demonstrated for this derivative using illustrative examples.