Novel Fractional Models Compatible with Real World Problems

Abstract

In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville-Caputo fractional conformable derivative and the modified form of this new definition. We utilize the sigma auxiliary parameter for preserving the dimension of physical quantities for newly defined fractional conformable vertical motion of a falling body problem in a resistant medium. The analytical solutions are obtained by iterating this new fractional integral and results are illustrated under different orders by comparison with the Liouville-Caputo fractional operator.