Photoconductivity,Antioxidant, and Antimicrobial Activities of Some Acenaphthenequinone Derivatives

Russian Journal of General Chemistry - Photoconductive acenaphthenequinone derivatives have been synthesized by a one-pot process of acenaphthenequinone with different aromatic hydrazides...     

Homotopy analysis method for fractional IVPs

In this paper, the homotopy analysis method is applied to solve linear and nonlinear fractional initial-value problems (fIVPs). The fractional derivatives are described by Caputo’s sense. Exact and/or approximate analytical solutions of the fIVPs are obtained. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.     

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.     

Structural,luminescence and biological studies of trivalent lanthanide complexes with N,N′-bis(2-hydroxynaphthylmethylidene)-1,3-propanediamine Schiff base ligand

New eight lanthanide metal complexes were prepared. These complexes were characterized by elemental analysis, molar conductivity measurements, spectral analysis (¹H NMR, FT-IR, UV–vis), luminescence and thermal gravimetric analysis. All Ln(III) complexes were 1:1 electrolytes as established by their molar conductivities. The microanalysis and spectroscopic analysis revealed eight-coordinated environments around lanthanide ions with two nitrate ligands behaving in a bidentate manner. The other four positions were found to be occupied with tetradentate L_III ligand. Tb–L_III and Sm–L_III complexes exhibited characteristic luminescence emissions of the central metal ions and this was attributed to efficient energy transfer from the ligand to the metal center. The L_III and Ln–L_III complexes showed antibacterial activity against a number of pathogenic bacteria.     

Numerical methods for nonlinear partial differential equations of fractional order

In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order.     

On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras

In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving Weyl-Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs.     

A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

In this article, a novel numerical method is proposed for nonlinear partial differential equations with space- and time-fractional derivatives. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. Results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order.     

Numerical solutions of the space‐time fractional advection‐dispersion equation

Fractional advection‐dispersion equations are used in groundwater hydrologhy to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper we present two reliable algorithms, the Adomian decomposition method and variational iteration method, to construct numerical solutions of the space‐time fractional advection‐dispersion equation in the form of a rabidly convergent series with easily computable components. The fractional derivatives are described in the Caputo sense. Some examples are given. Numerical results show that the two approaches are easy to implement and accurate when applied to space‐time fractional advection‐dispersion equations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Chromatographic behavior of doxylamine succinate, phenylpropanolamine hydrochloride, chlorpheniramine maleate, dextromethorphan hydrobromide, paracetamol, and guaifenesin in ion pair reverse-phase high performance liquid chromatography

A study of the chromatographic behavior of some cough syrup ingredients has led to the optimum chromatographic separation of four ingredients (doxylamine succinate, phenylpropanolamine hydrochloride, chlorpheniramine maleate, and dextromethorphan hydrobromide). The paracetamol and guaifenesin were overlapping under all chromatographic conditions. The application of 1% chlorotrimethylsilane in methanol to the column (Partisil 5 CCS/C₈) was found to improve the column efficiency significantly. This separation can be applied for the analysis of cough syrup for these ingredients after a study of the interferences due to normal excipients.²     

Analytic and approximate solutions of the space- and time-fractional telegraph equations

The Adomian decomposition method is used to obtain analytic and approximate solutions of the space-and time-fractional telegraph equations. The space- and time-fractional derivatives are considered in the Caputo sense. The analytic solutions are calculated in the form of series with easily computable terms. Some examples are given. The results reveal that the Adomian method is very effective and convenient.