New Approach To A Generalized Fractional Integral

Details New Approach To A Generalized Fractional Integral New Approach To A Generalized Fractional Integral

2010-10-05

arxiv.org/abs/1010.0742v2

Appl. Math. Comput. Vol 218, Issue 3, 1 October 2011, Pages 860-865

Mathematics

Classical Analysis and ODEs

12 pages, 2 figures, Submitted to : Applied Mathematics and Computations

Scientific paper

10.1016/j.amc.2011.03.062

The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases. Conditions are given for such a generalized fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for the above operator is also proved. Finally, we give a general definition of the Fractional derivatives.

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