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.
Trapezoid-type inequality, fractional conformable integrals, fractional conformable derivatives, fractional calculus, convex function
HEZENCİ, FATİH and BUDAK, HÜSEYİN
"Novel results on trapezoid-type inequalities for conformable fractional integrals,"
Turkish Journal of Mathematics: Vol. 47:
2, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss2/3