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Hilbert-Pachpatte type fractional integral inequalities. (English) Zbl 1165.26320
Summary: We present here very general weighted univariate and multivariate Hilbert-Pachpatte type integral inequalities. These involve Caputo and Riemann-Liouville fractional derivatives and fractional partial derivatives of the mentioned types.
MSC:
26D15Inequalities for sums, series and integrals of real functions
26A33Fractional derivatives and integrals (real functions)
References:
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[2]Pachpatte, B. G.: Inequalities similar to the integral analogue of Hilbert’s inequalities, Tamkang journal of mathematics 30, No. 1, 139-146 (1999) · Zbl 0962.26006
[3]Dragomir, S. S.; Kim, Y. -H.: Hilbert–Pachpatte type integral inequalities and their improvement, Journal of inequalities in pure and applied mathematics 4, No. 1 (2003) · Zbl 1020.26014 · doi:http://jipam-old.vu.edu.au/v4n1/
[4]Handley, G. D.; Koliha, J. J.; Pecaric, J.: Hilbert–Pachpatte type integral inequalities for fractional derivatives, Fractional calculus applied analysis 4, No. 1, 37-46 (2001) · Zbl 1030.26012
[5]Handley, G. D.; Koliha, J. J.; Pecaric, J.: New Hilbert–Pachpatte type integral inequalities, Journal of mathematical analysis and applications 257, 238-250 (2001) · Zbl 0988.26013 · doi:10.1006/jmaa.2000.7350
[6]Pachpatte, B. G.: On two new multidimensional integral inequalities of the Hilbert type, Tamkang journal of mathematics 31, 123-129 (2000) · Zbl 0991.26009
[7]Kai DietheIm, Fractional differential equations. On line: http://www.tu-bs.de/ diethelm/lehre/f-dgl02/fde-skript.ps.gz
[8]G. Anastassiou, Fractional Poincaré type inequalities, Indian Journal of Mathematics (2008) (in press)
[9]G. Anastassiou, Caputo fractional multivariate opial type inequalities on spherical shells, in: George Anastassiou (Ed.), The Proceedings of ”AMAT 2008”, an International Conference in ”Applied Mathematics and Approximation Theory”, University of Memphis, Memphis, USA, October 11–13, 2008, Eudoxus Press (in press)
[10]Anastassiou, G.: Hilbert–Pachpatte type general integral inequalities, Applicable analysis 86, No. 8, 945-961 (2007) · Zbl 1132.26308 · doi:10.1080/00036810701460818
[11]Anastassiou, G.: Hilbert–Pachpatte type general multivariate integral inequalities, International journal of applied mathematics 20, No. 4, 549-573 (2007) · Zbl 1157.26300
[12]Aliprantis, C.; Burkinshaw, O.: Principles of real analysis, (1998) · Zbl 1006.28001