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Full-Text Articles in Physical Sciences and Mathematics
A Study On Conformable Fractional Version Of Bullen-Type Inequalities, Fati̇h Hezenci̇, Hüseyi̇n Budak, Hasan Kara
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
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.
Some Remarks On Parameterized Inequalities Involving Conformable Fractional Operators, Ci̇han Ünal, Fati̇h Hezenci̇, Hüseyi̇n Budak
Some Remarks On Parameterized Inequalities Involving Conformable Fractional Operators, Ci̇han Ünal, Fati̇h Hezenci̇, Hüseyi̇n Budak
Turkish Journal of Mathematics
In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems.