An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative

Abstract A fractional derivative is a temporally nonlocal operation which computationally intensive due to inclusion of the accumulated contribution function values at past times. In order lessen computational load while maintaining accuracy derivative, novel numerical method for Caputo proposed. The present adaptive memory significantly reduces requirement storing time points and also improves by calculating convolution weights can be non-uniformly distributed in time. superior previously reported methods identified deriving errors analytically. sub-diffusion process time-fractional diffusion equation simulated demonstrate as well efficiency method.