SM-Algorithms for Approximating the Variable-Order Fractional Derivative of High Order

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Moghaddam, B. P.^{a; *} | Machado, J. A. T.^b

Affiliations: [a] Department of mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. parsa@liau.ac.ir | [b] Department of Electrical Engineering, Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, Porto 4249-015, Portugal. jtm@isep.ipp.pt

Correspondence: [*] Department of mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Abstract: In this paper we discuss different definitions of variable-order derivatives of high order and we propose accurate and robust algorithms for their approximate calculation. The proposed algorithms are based on finite difference approximations and B-spline interpolation. We compare the performance of the algorithms by experimental convergence order. Numerical examples are presented demonstrating the efficiency and accuracy of the proposed algorithms.

Keywords: Fractional calculus, Variable-order derivative, Spline approximation, Finite difference approximation, Convergence order, Numerical method

DOI: 10.3233/FI-2017-1493

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 293-311, 2017