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

DOI10.1515/FCA-2021-0058zbMath1498.65034arXiv1711.10071OpenAlexW2769613894MaRDI QIDQ2059218

Donghyun You, Daegeun Yoon

Publication date: 13 December 2021

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.10071

zbMATH Keywords

fractional differential equationsCaputo fractional derivativeadaptive memory method

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Numerical differentiation (65D25) Numerical integration (65D30)

Cites Work

• Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory
• Application of fractional calculus to ultrasonic wave propagation in human cancellous bone
• Convolution quadrature and discretized operational calculus. I
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• An efficient algorithm for the evaluation of convolution integrals
• Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
• Fast Convolution for Nonreflecting Boundary Conditions
• Fractional differentiation matrices with applications
• The numerical solution of fractional differential equations: speed versus accuracy

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