Abstract Recently, Anderson and Ulness [Adv. Dyn. Syst. Appl. 10, 109 (2015)] utilized the
concept of the proportional derivative controller to modify the conformable derivatives. In …

On more general forms of proportional fractional operators Skip to content Should you have
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We prove new Hermite‐Hadamard inequalities for conformable fractional integrals by using
convex function, s‐convex, and coordinate convex functions. We prove new Montgomery …

In this article, we present some new properties of the fractional proportional derivatives of a
function with respect to a certain function. We use a modified Laplace transform to find the …

In this paper, first, we prove an identity for conformable fractional integrals. Second, by using
this identity we will present some integral inequalities connected with the left hand side of …

Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this
paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann …

In this paper, we provide a new version for the Gronwall inequality in the frame of the
generalized proportional fractional derivative. Prior to the main results, we introduce the …

In this paper first, we prove some new generalizations of Hermite-Hadamard type
inequalities for the convex function f and for (s, m)-convex function f in the second sense in …

This article studies the existence theory of an innovation type of generalized proportional
fractional differential equations with the assistance of the technique of Kuratowski measure …

In this work, we present a new type of fractional derivatives (FD) involving exponential
cotangent function in their kernels called Riemann–Liouville D σ, γ and Caputo cotangent …