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Several Results of Fractional Derivatives in Dʹ(R+)

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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

$$y\left( x \right) + \frac{\lambda }{{\Gamma \left( { - \alpha } \right)}}\int_0^x {\frac{{y\left( \varsigma \right)}}{{{{\left( {x - \varsigma } \right)}^{\alpha + 1}}}}d\varsigma } = \delta \left( x \right),$$

where Re α > 0

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Authors and Affiliations

  1. Department of Mathematics and, Computer Science Brandon University, Brandon, Manitoba, RγA 6A9, Canada

    Chenkuan Li

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  1. Chenkuan Li
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Correspondence to Chenkuan Li.

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Li, C. Several Results of Fractional Derivatives in Dʹ(R+). FCAA 18, 192–207 (2015). https://doi.org/10.1515/fca-2015-0013

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  • DOI: https://doi.org/10.1515/fca-2015-0013

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