Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive?
Jocelyn Sabatier
Abstract
In the field of fractional calculus and applications, a current trend is to propose non-singular kernels for the definition of new fractional integration and differentiation operators. It was recently claimed that fractional-order derivatives defined by continuous (in the sense of non-singular) kernels are too restrictive. This note shows that this conclusion is wrong as it arises from considering the initial conditions incorrectly in (partial or not) fractional differential equations.
Topics & Concepts
Fractional calculusMathematicsOrder (exchange)Applied mathematicsField (mathematics)Calculus (dental)Differential (mechanical device)Mathematical analysisPure mathematicsPhysicsEconomicsFinanceThermodynamicsMedicineDentistryFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsAdvanced Control Systems Design