A Comparative Analysis of Conformable, Non-conformable, Riemann-Liouville, and Caputo Fractional Derivatives
Aabdessamad Aitbrahim, Jalila El Ghordaf, Abdelmajid El Hajaji, Khalid Hilal, Juan E. Nápoles Valdés
Abstract
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 $1/2 < \alpha < 1$.
Topics & Concepts
Conformable matrixMathematicsRiemann hypothesisPure mathematicsMathematical analysisApplied mathematicsPhysicsQuantum mechanicsNonlinear Differential Equations AnalysisMathematical functions and polynomialsDifferential Equations and Boundary Problems