Comparative performance of L-fractional versus Caputo derivatives in applications

Determine whether L-fractional differential equations provide better performance than Caputo fractional differential equations in specific modeling tasks by evaluating smoothness, finite initial slopes, dimensional consistency, and differential-form interpretation using applied models, simulations, and data fitting.

Background

The paper introduces the L-fractional derivative as a normalized variant of the Caputo derivative with advantageous properties such as smooth solutions, finite initial slopes, and standard velocity units. The authors propose assessing whether these theoretical advantages translate into improved performance in practical modeling scenarios.