A Discretization of Caputo Derivatives with Application to Time Fractional SDEs and Gradient Flows
A Discretization of Caputo Derivatives with Application to Time Fractional SDEs and Gradient Flows
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of the corresponding implicit schemes, are proved by its linkage to Volterra integrals with completely monotone kernels. We then apply …