Fractional Conformable Self Adjoint Operator Analytic Inequalities
We present here conformable fractional self adjoint operator comparison, Poincaré, Sobolev, Ostrowski and Opial type inequalities. At first we give right and left conformable fractional representation formulae in the self adjoint operator sense. Operator inequalities are based in the self adjoint operator order over a Hilbert space. See also .
- 2.G.A. Anastassiou, Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators, Studies in Systems, Decision and Control (Springer, Heidelberg, 2018)Google Scholar
- 3.G.A. Anastassiou, Conformable fractional self adjoint operator analytic inequalities, submitted for publication, 2019Google Scholar
- 4.G.A. Anastassiou, Conformable fractional inequalities, in Functional Equations and Analytic Inequalities, ed. by G. Anastassiou, J. Rassias (Springer, New York, 2020), accepted for publicationGoogle Scholar
- 5.S.S. Dragomir, Inequalities for functions of selfadjoint operators on Hilbert spaces (2011), www.ajmaa.org/RGMIA/monographs/InFuncOp.pdf
- 7.T. Furuta, J. Mićić Hot, J. Pečaric, Y. Seo, Mond-Pečaric Method in Operator Inequalities, Inequalities for Bounded Self adjoint Operators on a Hilbert Space (Element, Zagreb, 2005)Google Scholar
- 9.R. Khalil, M. Al. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)Google Scholar