A Comparative Analysis of Conformable, Non-conformable, Riemann-Liouville, and Caputo Fractional Derivatives

• Published in: European journal of pure and applied mathematics Vol. 17; no. 3; pp. 1842 - 1854
• Main Authors: Aitbrahim, Aabdessamad, Ghordaf, J. El, El Hajaji, A., Hilal, K., Valdes, J. E.Napoles
• Format: Journal Article
• Language: English
• Published: 31-07-2024
• ISSN: 1307-5543; 1307-5543
• DOI: 10.29020/nybg.ejpam.v17i3.5237

This study undertakes a comparative analysis of the non conformable and  conformable fractional derivatives alongside the Riemann-Liouville and Caputo fractional derivatives. It examines their efficacy in solving fractional ordinary differential equations and explores their applications in physics through numerical simulations. The findings suggest that the conformable fractional derivative emerges as a promising substitute for the non conformable, Riemann-Liouville and Caputo fractional derivatives within the range of order  $\alpha $ where $1/2 < \alpha < 1$.