Caputo–Hadamard Fractional Derivatives of Variable Order. (2nd January 2017)

• Record Type: Journal Article
• Authors: Almeida, Ricardo
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 1(2017)
• Page Start: 1
• Page End: 19
• Publication Date: 2017-01-02
• Subjects: Caputo fractional derivative -- expansion formulas -- fractional calculus -- Hadamard fractional derivative -- variable fractional order; 26A33 -- 33F05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1217880
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we present three types of Caputo–Hadamard derivatives of variable fractional order and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained and an estimation for the error is given. At the end, we compare the exact fractional derivative of a concrete example with some numerical approximations.