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Fractional Calculus and Applied Analysis

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Band 18, Heft 1


Several Results of Fractional Derivatives in Dʹ(R+)

Chenkuan Li
Online erschienen: 10.02.2015 | DOI: https://doi.org/10.1515/fca-2015-0013


In this paper, we define fractional derivative of arbitrary complex order of the distributions concentrated on R+, based on convolutions of generalized functions with the supports bounded on the same side. Using distributional derivatives, which are generalizations of classical derivatives, we present a few interesting results of fractional derivatives in D'(R+), as well as the symbolic solution for the following differential equation by Babenko's method


where Re α>0

MSC 2010: 46F10; 26A33

Key Words and Phrases: distribution; convolution; Dirac delta function; Abel's equation; Gamma function; Caputo derivative and Riemann-Liouville derivative


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Erhalten: 18.06.2014

Online erschienen: 10.02.2015

Quellenangabe: Fractional Calculus and Applied Analysis, Band 18, Heft 1, Seiten 192–207, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0013.

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