New approach to a generalized fractional integral
Copyright policy )New approach to a generalized fractional integral
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.
12 pages, 2 figures, Submitted to : Applied Mathematics and Computations
- Southern Illinois University Carbondale United States
Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, Hadamard fractional derivative, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Riemann-Liouville fractional derivative, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 26A33, semigroup property
Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, Hadamard fractional derivative, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Riemann-Liouville fractional derivative, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 26A33, semigroup property
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