A novel approach of variable order derivative: Theory and Methods

In order to solve problems posed while using the concept of fractional variable order derivative, we introduce in this work a novel fractional variable order derivative. Our derivative has no singular kernel, this allows it to well-describe the effect of memory. We present the relationship between the new derivative with the well-known integral transforms. We present exact solution of some basic associated differential equations. We presented the numerical approximation of the derivative for first and second order approximation.