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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 18, Issue 1

Issues

Several Results of Fractional Derivatives in Dʹ(R+)

Chenkuan Li
  • Corresponding author
  • Department of Mathematics and Computer Science Brandon University, Brandon, Manitoba, RγA 6A9-CANADA
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Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0013

Abstract

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

y(x)+λΓ(-α)0xy(σ)(x-σ)α+1dσ=δ(x),

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

References

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About the article

Received: 2014-06-18

Published Online: 2015-02-10


Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 192–207, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0013.

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[1]
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[2]
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