New definition of fractional derivative included Mittag-Leffler function of conformable type

Abstract

In this paper a new definitionn of fractional derivative and fractional integral in the sense ofconformable derivative type is presented. This form of definition shows that it is more compatible withclassical natural definition of derivative and is more convinient fractional derivative one. We will definethis for 0 ≤ α < 1 and n − 1 ≤ α < n and further, if α = 1 the definition coincides with the classicaldefinition of derivative of first order.

Keywords

• mittag-leffler function
• fractional derivative
• conformable derivative