The theory of UD derivative and its applications

Abstract

The sole purpose of this study is to propose a new concept to fractional derivative as Ujlayan-Dixit derivative in the classical sense using limit approach. The parameter α of the derivative is confined within a closed unit interval. It is easy to apply and generates a convex combination of function and its derivative. We observe its geometrical behavior and see, how it is different from the previous definitions of the concerned derivatives. It works as an improved form of Conformable fractional derivative and fulfill the meaningful gaps. Some basic properties of calculus like continuity, differentiability, Mean Value theorem, Comparison theorem and some numerical have discussed.