Khalil Conformable fractional derivative and its applications to population growth and body cooling models

Abstract

The objective of this article is to develop some results on conformable fractional derivatives, specifically the one known as Khalil's conformable fractional derivative. Its origin, properties, comparisons with other fractional derivatives and some applications on population grow and Newton law of cooling models are studied.

Extracting the Ultimate New Soliton Solutions of Some Nonlinear Time Fractional PDEs via the Conformable Fractional Derivative

“…We note that fractional-order derivatives [13,14] are difficult to deal with analytically, primarily those that describe real-world operations, and investigators sometimes must depend on the numerical approach to solve these equations. Many investigators have used various operators of fractional derivatives like Caputo-Fabrizio [15,16], Riemann-Liouville [17,18], conformable fractional derivatives [19,20], etc., in fractional-order PDEs of any system. One of the most familiar fractional-order PDE is the nonlinear KGE [21], which has widespread implementations in condensed-type matter physics, nonlinear optics, quantum mechanics, etc., and is also suitable for modeling real-world occurrences.…”