A new approch to fractional derivatives

Abstract EN

A derivative of a function of order, for any real number (called a fractional derivative) is the subject of this paper.

In this paper a new definition of the fractional derivative of order of a function is given.

This new definition will depend on the formal power series summation.

We used this new definition to find the fractional derivative of the constant functions and the polynomials.

The result was the same result by using the known definitions of fractional derivatives until now.

Also, we proved properties of the fractional derivative.

Finally, we conjecture that the fractional derivative of order of the exponential function is the exponential function and this will help us in finding the fractional derivatives of the trigonometric functions and hyperbolic functions.

The purpose of this research is to find an easy way to derive the fractional derivatives for the functions, since every differentiable function can be represented by power series expansion, even if the radius of convergence of the power series is 0, we believe that this method will give nice results which can be used in the application.