Some Opial type inequalities for conformable fractional integrals

On generalization conformable fractional integral inequalities

“…Assume in additional that r is non-decreasing and r(t) ≤ t for t ≥ 0. If u ∈ C (R + , R + ) satisfies Combine the above inequality with u(t) ≤ k(t) + m(t)z(t) this imply (14). The proof is complete.…”

“…If we take (t) = 0 in Theorem 3.1, then Theorem 3.1 reduces to Theorem 4 which has been proved by Sarikaya in [14]. Theorem 3.4.…”

“…The below theorem is the generalization of Theorem 2.10 of [5] which the detailed proof can be found in [14].…”

Inequalities for Katugampola conformable partial derivatives

“…This completes the proof. This inequality (2.16) is just a two-dimensional generalization of the following inequality which was established in [21]:…”

“…Recently, some new Opial's inequalities for the conformable fractional integrals have been established (see [19][20][21][22]). In the paper, we introduce two new concepts of Katugampola conformable partial derivatives and α-conformable integrals.…”