Anastassiou, George A. Hilbert-Pachpatte type fractional integral inequalities. (English) Zbl 1165.26320 Math. Comput. Modelling 49, No. 7-8, 1539-1550 (2009). 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. Cited in 7 Documents MSC: 26D15 Inequalities for sums, series and integrals 26A33 Fractional derivatives and integrals Keywords:univariate and multivariate Hilbert inequality; univariate and multivariate Hilbert-Pachpatte inequality; caputo fractional derivative; Riemann-Liouville fractional derivative; fractional partial derivatives PDFBibTeX XMLCite \textit{G. A. Anastassiou}, Math. Comput. Modelling 49, No. 7--8, 1539--1550 (2009; Zbl 1165.26320) Full Text: DOI References: [1] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1934), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK · Zbl 0010.10703 [2] Pachpatte, B. G., Inequalities similar to the integral analogue of Hilbert’s inequalities, Tamkang Journal of Mathematics, 30, 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, 1 (2003), Article 16. · Zbl 1020.26014 [4] Handley, G. D.; Koliha, J. J.; Pecaric, J., Hilbert-Pachpatte type integral inequalities for fractional derivatives, Fractional Calculus & Applied Analysis, 4, 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 [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; 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); 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); 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, 8, 945-961 (2007) · Zbl 1132.26308 [11] Anastassiou, G., Hilbert-Pachpatte type general multivariate integral inequalities, International Journal of Applied Mathematics, 20, 4, 549-573 (2007) · Zbl 1157.26300 [12] Aliprantis, C.; Burkinshaw, O., Principles of Real Analysis (1998), Academic Press: Academic Press San Diego, New York · Zbl 1006.28001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.