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research-article

On finite part integrals and Hadamard-type fractional derivatives

[+] Author and Article Information
Li Ma

School of Mathematics, Hefei University of Technology, Hefei 230009, China
mali20062787@163.com

Changpin Li

Department of Mathematics, Shanghai University, Shanghai 200444, China
lcp@shu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4037930 History: Received July 18, 2017; Revised August 29, 2017

Abstract

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense, that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral which does not exist. Besides, our results also cover that some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.

Copyright (c) 2017 by ASME
Topics: Space
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