Starting from second-order conditions for C scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof...

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

The modification of the Clarke generalized subdiNerentia1 due to Michel and Penot is a useful tool in determining differentiability properties for certain classes of real functions on a normed linear space. The Glteaux differentiability of any real function can be deduced from the GBteaux differentiability of the norm if the function has a directional derivative which attains a constant related...

In this study, a derivative method is applied for the determination of dye concentration in fabrics dyed with tricomponent dye mixtures. The reflectance of spectra of the samples were recorded between 400 and 700 nm. Initially, the obtained (K/S) spectra were divided by the spectrum of a standard sample dyed with two of the components in the ternary mixture and the derivative spectra were calcu...

two sensitive spectrophotometric methods are presented for the assay of repaglinide in bulkdrug and in formulations using methyl orange, as reagents. oxidant by reacting with a fixedamount of either methyl orange and measuring the absorbance at 485.2 nm (method-i) andmeasuring the absorbance at 618.9 nm (method-ii). developed method is based on the formationof extractable colored complex of dru...

In this paper, we establish the existence and uniqueness result of the linear Schrodinger equation with Marchaud fractional derivative in Colombeau generalized algebra. The purpose of introducing Marchaud fractional derivative is regularizing it in Colombeau sense.

in this paper, we establish the existence and uniqueness result of the linear schrodinger equation with marchaud fractional derivative in colombeau generalized algebra. the purpose of introducing marchaud fractional derivative is regularizing it in colombeau sense.