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Get Access to Full TextIn this paper, we define fractional derivative of arbitrary complex order of the distributions concentrated on , 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 , as well as the symbolic solution for the following differential equation by Babenko's method
,
where Re
Key Words and Phrases: distribution; convolution; Dirac delta function; Abel's equation; Gamma function; Caputo derivative and Riemann-Liouville derivative
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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.
© 2015 Diogenes Co., Sofia.
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