Consensus of classical and fractional inequalities having congruity on time scale calculus

Author:

Sahir Muhammad Jibril Shahab1

Affiliation:

1. University of Sargodha , Sub-Campus Bhakkar, Pakistan ; Faculty of Mathematics, Department of Mathematics , GHSS, 67/ML, Bhakkar , Pakistan

Abstract

Abstract In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.

Publisher

Walter de Gruyter GmbH

Reference22 articles.

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2. [2] R. P. Agarwal, D. O’Regan, S. H. Saker, Dynamic inequalities on time scales, Springer International Publishing, Cham, Switzerland, 2014.10.1007/978-3-319-11002-8

3. [3] G. A. Anastassiou, Principles of delta fractional calculus on time scales and inequalities, Mathematical and Computer Modelling, vol. 52, no. 3-4, 2010, 556-566.10.1016/j.mcm.2010.03.055

4. [4] G. A. Anastassiou, Foundations of nabla fractional calculus on time scales and inequalities, Computers & Mathematics with Applications, vol. 59, no. 12, 2010, 3750-3762.10.1016/j.camwa.2010.03.072

5. [5] G. A. Anastassiou, Integral operator inequalities on time scales, International Journal of Difference Equations, vol. 7, no. 2, 2012, 111-137.

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