Lorenzo, C.F. and Hartley, T.T. (2008) Initialization of Fractional-Order Operators and Fractional Differential Equations. Journal of Computational and Nonlinear Dynamics, 3, Article ID: 021101.
https://doi.org/10.1115/1.2833585

has been cited by the following article:

• TITLE: Conformable and Caputo’s Derivatives in Generalized Viscoelastic Models

  AUTHORS: Jorge Fujioka, Rosalío Fernando Rodríguez, Áurea Espinosa-Cerón

  KEYWORDS: Conformable Derivatives, Caputo’s Derivatives, Fractional Derivatives, Viscoelastic Fluids, Hydrodynamic Fluctuations

  JOURNAL NAME: Applied Mathematics, Vol.14 No.9, September 15, 2023

  ABSTRACT: We study two generalized versions of a system of equations which describe the time evolution of the hydrodynamic fluctuations of density and velocity in a linear viscoelastic fluid. In the first of these versions, the time derivatives are replaced by conformable derivatives, and in the second version left-handed Caputo’s derivatives are used. We show that the solutions obtained with these two types of derivatives exhibit significant similarities, which is an interesting (and somewhat surprising) result, taking into account that the conformable derivatives are local operators, while Caputo’s derivatives are nonlocal operators. We also show that the solutions of the generalized systems are similar to the solutions of the original system, if the order α of the new derivatives (conformable or Caputo) is less than one. On the other hand, when α is greater than one, the solutions of the generalized systems are qualitatively different from the solutions of the original system.