New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators

Abstract

At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators.

Some New Jensen–Mercer Type Integral Inequalities via Fractional Operators

“…In the remainder of this paper, we aim to give generalizations of Hermite-Hadamard inequality (4) via non-conformable fractional integrals defined by Nápoles et al in [26].…”

On the Oscillatory Behavior of Some Qeneralized Differential Equation

“…, we obtain the local derivatives of [25], [39] and [33], respectively. On the other hand, considering Φ(τ, α) = E 1,1 ((1 − α)τ ) = e (α−1)τ we obtain a conformable derivative not yet reported in the literature.…”

Note on the conformable boundary value problems: Sturm’s theorems and Green’s function

“…The difference between conformable fractional derivative and non-conformable fractional derivative is that the tangent line angle is conserved in the conformable one, while it is not conserved in the sense of nonconformable one [25] (see also [26,34,36,37] for more new related results about this newly proposed definition of non-conformable fractional derivative). The definition of non-conformable fractional derivative has been investigated and applied in various research studies and applications of physics and natural sciences such as the stability analysis, oscillatory character, and boundedness of fractional Liénard-type systems [27,28,33], analysis of the local fractional Drude model [29], Hermite-Hadamard inequalities [30], fractional Laplace transform [31], fractional logistic growth models [32], oscillatory character of fractional Emden-Fowler equation [35], asymptotic behavior of fractional nonlinear equations [38], and qualitative behavior of nonlinear differential equations [39]. This paper is organized as follows: In Sec.…”