Parallel correspondences of bi-conservative surfaces in E3 with fractional order derivative

Abstract

In this paper, we study the bi-conservative property of parallel revolution surface in Euclidean 3-space E3 using a new definition of fractional derivative known as the conformable fractional derivative, which is a natural extension of the usual derivative and its definition is the simplest and the most natural definition of a fractional derivative which satisfies formulas of derivative of the product and the quotient of two functions and which has a simpler chain rule depending just on the basic limit definition of the derivative (see, R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh. A new definition of fractional derivative, Journal of Computational and Aapplied Mathematics, 264, 65 70, 2014).