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2 2019

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Refinements of the Hermite-Hadamard inequality for co-ordinated convex mappings

Budak Huseyin, Usta Fuat, Sarikaya Mehmet Zeki

Journal of Applied Analysis

2019

Vol. 25, nr 1

73--81

This paper is motivated by the recent progress on the Hermite-Hadamard inequality for convex functions defined on the bounded closed interval, obtained by Z. Pavić [Z. Pavić, Improvements of the Hermite-Hadamard inequality, J. Inequal. Appl. 2015 (2015), Article ID 222]. As a generalization, we obtained a new refinement of the Hermite-Hadamard inequality for co-ordinated convex functions defined on the rectangle.

The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

Usta Fuat, Sarıkaya Mehmet Zeki

Demonstratio Mathematica

2019

Vol. 52, nr 1

204--212

In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.