Initial value problems should not be associated to fractional model descriptions whatever the derivative definition used

DOI10.3934/math.2021657OpenAlexW3187729430MaRDI QIDQ2671143

Christophe Farges, Jocelyn Sabatier

Publication date: 3 June 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2021657

zbMATH Keywords

initial conditionsmemoryRiemann-Liouville definitionCaputo definitionGrünwald-Letnikov definitiontime fractional derivative

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Fractional derivatives and integrals (26A33)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Riemann-Liouville and Caputo derivatives
• How to impose physically coherent initial conditions to a fractional system?
• On the initial conditions in continuous-time fractional linear systems
• System initial conditions vs derivative initial conditions
• Numerical solution of fractional differential equations: a survey and a software tutorial
• A review of definitions for fractional derivatives and integral
• Comments on the description and initialization of fractional partial differential equations using Riemann-Liouville's and Caputo's definitions
• Extinction for a discrete competition system with the effect of toxic substances
• Fractional-order derivatives defined by continuous kernels are too restrictive
• Role of prehistories in the initial value problems of fractional viscoelastic equations
• An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions
• An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense
• Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market
• Mathematical Systems Theory I
• Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing
• A generalized fractional-order elastodynamic theory for non-local attenuating media
• Analysis of fractional differential equations