Novel Fractional Models Compatible with Real World Problems

• Main Authors: Ramazan Ozarslan, Ahu Ercan, Erdal Bas
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Fractal and Fractional
• Subjects: fractional derivative; vertical motion of falling body problem; Malthusian growth equation
• Online Access: https://www.mdpi.com/2504-3110/3/2/15

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 <inline-formula> <math display="inline"> <semantics> <mi>σ</mi> </semantics> </math> </inline-formula> 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.