A Novel Definition of The Derivative and Integral of Fractional Type with Applications

Abstract

A new modified definition of the fractional derivative and fractional integral of conformable type has been presented that matches the previous classical definitions. A comparison was made between the new definition and the previous definitions, and it was found that the new definition is more useful, important, and appropriate for polynomial functions, where . Also, if , the new definition is similar to the classical definition of the derivative. The proposed definition was discussed and some applications were presented to some functions and fractional differential equations. A solution to the  powers was proposed and the integration rule was proven using upper and lower values and applied in this study