A regularization method for Caputo fractional derivatives
in the Banach space L∞[0, T]
Authors: Nguyen Van Duc, Nguyen Thi Phong
Numerical Algorithms
: 95 : 1033-1053
Publishing year: 7/2023
This work is dedicated to the investigation of aregularizationmethodfor the problem of
determining Caputo fractional derivatives of a function in the Banach space L∞[0, T].
This regularization method is based on the approximation of the first-order derivative
of the function by the solution of a well-posed problem depending on a regularization
parameter. We then discuss the Hölder type stability results for the method according
to two choice rules for the regularization parameter, which are an a priori parameter
choice rule and an a posteriori parameter choice rule. Some numerical examples are
provided
Caputo fractional derivative · Ill-posed problems · Regularization · A priori parameter choice rule · A posteriori parameter choice rules · Error estimates
