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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.

26D15Inequalities for sums, series and integrals of real functions
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
[1] Hardy, G. H.; Littlewood, J. E.; Polya, G.: Inequalities, (1934) · Zbl 0010.10703
[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 · http://jipam-old.vu.edu.au/v4n1/
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[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)
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[10] Anastassiou, G.: Hilbert--Pachpatte type general integral inequalities, Applicable analysis 86, No. 8, 945-961 (2007) · Zbl 1132.26308 · doi:10.1080/00036810701460818
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[12] Aliprantis, C.; Burkinshaw, O.: Principles of real analysis, (1998) · Zbl 1006.28001