| Title | FRACTIONAL MULTIVARIATE OPIAL TYPE INEQUALITIES OVER SPHERICAL SHELLS |
| Publication Type | Journal Article |
| Year of Publication | 2007 |
| Authors | Anastassiou, GA |
| Secondary Title | Communications in Applied Analysis |
| Volume | 11 |
| Issue | 2 |
| Start Page | 201 |
| Pagination | 233 |
| Date Published | 04/2007 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 26A33, 26D10, 26D15 |
| Abstract | Here is introduced the concept of multivariate fractional differentiation especially of the fractional radial differentiation, by extending the univariate definition of Canavati [11]. Then we produce Opial type nequalities over compact and convex subsets of RN, N ≥ 2, mainly over spherical shells, studying the problem in all possibilities. Our results involve one, or two, or more functions.
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| URL | http://www.acadsol.eu/en/articles/11/2/5.pdf |
| Short Title | Fractional Multivariate Opial Type Inequalities |
| Refereed Designation | Refereed |
| Full Text | References[1] R.P. Agarwal and P.Y.H. Pang, Opial Inequalities with Applications in Differential and Difference Equations, Kluwer, Dordrecht, London, 1995.
[2] G.A. Anastassiou, Multivariate fractional Taylor’s formula, Communications in Applied Analysis 11 (2006), no. 2, To Appear. [3] G.A. Anastassiou, Fractional Opial inequalities for several functions with applications, J. Comput. Anal. Appl., 7 (2005), no. 3, 233-259. [4] G.A. Anastassiou, Opial type inequalities involving fractional derivatives of two functions and applications, Comput. Math. Appl., 48 (2004), no-s: 10-11, 1701-1731. [5] G.A. Anastassiou, Quantitative Approximations, Chapman and Hall/CRC, Boca Raton, New York, 2001. [6] G.A. Anastassiou, Opial type inequalities involving functions and their ordinary and fractional derivatives, Commun. Appl. Anal., 4 (2000), no. 4, 547-560. [7] G.A. Anastassiou, Opial type inequalities involving fractional derivatives of functions, Nonlinear Stud., 6 (1999), no. 2, 207-230. [8] G.A. Anastassiou, General fractional Opial type inequalities, Acta Appl. Math., 54 (1998), no. 3, 303-317. [9] G.A. Anastassiou and J.A. Goldstein, Fractional Opial type inequalities and fractional differential equations, Results Math., 41 (2002), no-s. 3-4, 197-212. [10] P.R. Beesack, On an integral inequality of Z. Opial, Trans. Amer. Math. Soc., 104 (1962), 470-475. [11] I.A. Canavati, The Riemann- Liouville Integral, Nieuw Archief Voor Wiskunde, 5 (1987), no. 1, 53-75. [12] Z. Opial, Sur une inegalite, Ann. Polon. Math., 8 (1960), 29-32. [13] D. Willett, The existence-uniqueness theorem for an nth order linear ordinary differential equation, Amer. Math. Monthly, 75 (1968), 174-178. |