Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 218, Issue 3, Pages 860-865Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.03.062
Keywords
Generalized fractional integral; Generalized fractional derivative; Riemann-Liouville fractional derivative; Hadamard fractional derivative; Semigroup property
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The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form. Conditions are given for such a fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for the above operator is also proved. We give a general definition of the fractional derivatives and give some examples. (C) 2011 Elsevier Inc. All rights reserved.
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