## THE THEORY OF UD DERIVATIVE AND ITS APPLICATIONS

## THE THEORY OF UD DERIVATIVE AND ITS APPLICATIONS

*A. Dixit, A. Ujlayan*

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## 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 of the derivative is conned 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 dierent from the previous denitions of the concerned derivatives. It works as an improved form of Conformable fractional deriv- ative and fulll the meaningful gaps. Some basic properties of calculus like continuity, dierentiability, Mean Value theorem, Comparison theorem and some numerical have discussed.

## Keywords

Fractional derivative, conformable derivative, fractional dierential equations, UD derivative, fractional integral.