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New approach to a generalized fractional integral. (English) Zbl 1231.26008
Summary: 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. A semigroup property for the above operator is also proved. We give a general definition of fractional derivatives and give some examples.

MSC:
26A33 Fractional derivatives and integrals
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References:
[1] Butzer, P.L.; Kilbas, A.A.; Trujillo, J.J., Compositions of Hadamard-type fractional integration operators and the semigroup property, Journal of mathematical analysis and applications, 269, 387-400, (2002) · Zbl 1027.26004
[2] Butzer, P.L.; Kilbas, A.A.; Trujillo, J.J., Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, Journal of mathematical analysis and applications, 269, 1-27, (2002) · Zbl 0995.26007
[3] Hadamard, J., Essai sur l’etude des fonctions donnees par leur developpment de Taylor, Journal pure and applied mathematics, 4, 8, 101-186, (1892) · JFM 24.0359.01
[4] Kilbas, A., Hadamard-type fractional calculus, Journal of Korean mathematical society, 38, 6, 1191-1204, (2001) · Zbl 1018.26003
[5] Kilbas, A.A.; Trujillo, J.J., Hadamard-type integrals as G-transforms, Integral transforms and special functions, 14, 5, 413-427, (2003) · Zbl 1043.26004
[6] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., Theory and applications of fractional differential equations, (2006), Elsevier B.V. Amsterdam, Netherlands · Zbl 1092.45003
[7] Oldham, K.B.; Spanier, J., The fractional calculus, (1974), Academic Press New York · Zbl 0428.26004
[8] Podlubny, I., Fractional differential equations, (1999), Academic Press San Diego, California-USA · Zbl 0918.34010
[9] Samko, S.G.; Kilbas, A.A.; Marichev, O.I., Fractional integrals and derivatives, Theory and applications, (1993), Gordon and Breach Yverdon et alibi · Zbl 0818.26003
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