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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

TÜBİTAK

Journal

2023

Fractional conformable derivatives

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

A Study On Conformable Fractional Version Of Bullen-Type Inequalities, Fati̇h Hezenci̇, Hüseyi̇n Budak, Hasan Kara Jan 2023

A Study On Conformable Fractional Version Of Bullen-Type Inequalities, Fati̇h Hezenci̇, Hüseyi̇n Budak, Hasan Kara

Turkish Journal of Mathematics

In this paper, we give an equality for the case of differentiable convex functions involving conformable fractional integrals. Bullen-type inequalities for the conformable fractional integrals are established by using this equality. Some important inequalities are obtained by taking advantage of the convexity, the Hölder inequality and the power mean inequality. By using special choices, we present some known results in the literature. Furthermore, we give an example using a graph in order to show that our main results are correct.


Novel Results On Trapezoid-Type Inequalities For Conformable Fractional Integrals, Fati̇h Hezenci̇, Hüseyi̇n Budak Jan 2023

Novel Results On Trapezoid-Type Inequalities For Conformable Fractional Integrals, Fati̇h Hezenci̇, Hüseyi̇n Budak

Turkish Journal of Mathematics

This paper establishes an identity for the case of differentiable $s-$convex functions with respect to the conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by $s-$convex functions with the help of the conformable fractional integrals. Several important inequalities are acquired with taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Moreover, an example using graph is given in order to show that our main results are correct. By using the special choices of the obtained results, we present several new results connected with trapezoid-type inequalities.