Search

In the present work, the new iterative method with a combination of the Laplace transform of the Caputo's fractional derivative has been applied to the generalized (3 + 1) dimensional fractional perturbed Zakharov–Kuznetsov equation in a dusty plasma. The proposed method is applied without any discretization and linearization. The numerical and graphical results show the accuracy of the proposed method for nonlinear differential equations. Moreover, the methods are easy to implement and give the efficient approximate solutions. [ABSTRACT FROM AUTHOR]

In this paper, the implementation of the Fractional Variational iteration method (FVIM) is used to approximate the generalized fractional perturbed Zakharove-Kuznetsov equation. The obtained results show that the suggested approach is very efficient for dealing with various forms of differential equations of fractional order. The numerical comparison for the attained resolution is made through the q-homotopy analysis transmute manner (q-HATM) which confirms the convergence of the devised method. The applicability of the method is observed by applying the proposed technique to two numerical examples. Furthermore, the solutions obtained by the FVIM are completely well-matched with the solutions presented in the literature. [ABSTRACT FROM AUTHOR]

Within the context of fractional calculus, we investigate novel mathematical possibilities. In this context, using the fractional dispersion relations for the fractional wave equation, we explore a class of the generalized fractional wave equation numerically. Some important classes of differential equations in the theory of wave studies are Drinfeld–Sokolov–Wilson and Shallow Water equations. In this effort, the natural transform decomposition technique has been implemented to investigate the explicit result of fractional-order coupled schemes of Drinfeld–Sokolov–Wilson and Shallow Water coupled systems. The proposed method is obtained by coupling the Natural transform with the Adomian decomposition process. The current technique significantly works to find the approximate solution without any discretization or constraining parameter assumptions. The obtained numerical and graphical outcomes by the devised technique are compared with the available exact result to verify the convergence of the method. For mathematical calculations, the Mathematica software package is used. [ABSTRACT FROM AUTHOR]

Pseudomonas aeruginosa is one of the most antibiotic-resistant and opportunistic pathogens in immunocompromised and debilitated patients. It is considered the cause of most severe skin infections and is frequently found in hospital burn units. Due to its high antibiotic resistance, eliminating P. aeruginosa from skin infections is quite challenging. Therefore, this study aims to assess the novel in vitro antibacterial activity of methylene blue using a 635-nm diode laser to determine the effective power and energy densities for inhibition of P. aeruginosa. The strain was treated with various concentrations of methylene blue and 635-nm diode laser at powers of 300 mW/cm2 and 250 mW/cm2. The diode laser's potency in the photo-destruction of methylene blue and its degradation through P. aeruginosa were also evaluated. Colony-forming unit (CFU)/ml, fluorescence spectroscopy, optical density, and confocal microscopy were used to measure the bacterial killing effect. As a result, the significant decrease of P. aeruginosa was 2.15-log10, 2.71-log10, and 3.48-log10 at 60, 75, and 90 J/cm2 after excitation of MB for 240, 300, and 360 s at a power of 250 mW/cm2, respectively. However, a maximum decrease in CFU was observed by 2.54-log10 at 72 J/cm2 and 4.32-log10 at 90 and 108 J/cm2 after 300 mW/cm2 of irradiation. Fluorescence images confirmed the elimination of bacteria and showed a high degree of photo-destruction compared to treatment with methylene blue and light alone. In conclusion, MB-induced aPDT demonstrated high efficacy, which could be a potential approach against drug-resistant pathogenic bacteria. Key points: • Combination of methylene blue with 635-nm diode laser for antibacterial activity. • Methylene blue photosensitizer is employed as an alternative to antibiotics. • aPDT showed promising antibacterial activity against Pseudomonas aeruginosa. [ABSTRACT FROM AUTHOR]

Pseudomonas aeruginosa is one of the most antibiotic-resistant and opportunistic pathogens in immunocompromised and debilitated patients. It is considered the cause of most severe skin infections and is frequently found in hospital burn units. Due to its high antibiotic resistance, eliminating P. aeruginosa from skin infections is quite challenging. Therefore, this study aims to assess the novel in vitro antibacterial activity of methylene blue using a 635-nm diode laser to determine the effective power and energy densities for inhibition of P. aeruginosa. The strain was treated with various concentrations of methylene blue and 635-nm diode laser at powers of 300 mW/cm2 and 250 mW/cm2. The diode laser’s potency in the photo-destruction of methylene blue and its degradation through P. aeruginosa were also evaluated. Colony-forming unit (CFU)/ml, fluorescence spectroscopy, optical density, and confocal microscopy were used to measure the bacterial killing effect. As a result, the significant decrease of P. aeruginosa was 2.15-log10, 2.71-log10, and 3.48-log10 at 60, 75, and 90 J/cm2 after excitation of MB for 240, 300, and 360 s at a power of 250 mW/cm2, respectively. However, a maximum decrease in CFU was observed by 2.54-log10 at 72 J/cm2 and 4.32-log10 at 90 and 108 J/cm2 after 300 mW/cm2 of irradiation. Fluorescence images confirmed the elimination of bacteria and showed a high degree of photo-destruction compared to treatment with methylene blue and light alone. In conclusion, MB-induced aPDT demonstrated high efficacy, which could be a potential approach against drug-resistant pathogenic bacteria. Key points: • Combination of methylene blue with 635-nm diode laser for antibacterial activity. • Methylene blue photosensitizer is employed as an alternative to antibiotics. • aPDT showed promising antibacterial activity against Pseudomonas aeruginosa. [ABSTRACT FROM AUTHOR]

In this article, Fluorescence spectroscopy has been employed for the assessment of microbial load and it has been compared with the gold standard colony forming unit (CFU) and optical density (OD) methods. In order to develop a correlation between three characterization techniques, water samples of different microbial loads have been prepared by UVC disinfection method through an indigenously developed NUVWater sterilizer, which operates in close cycle flow configuration. A UV dose of 58.9 mJ/cm2 has been determined for 99.99% disinfection for a flow rate of 0.8 l/min. The water samples were excited at 270 nm which results in the tryptophan like fluorescence at 360 nm that decreases gradually with increase of UVC dose, indicating the bacterial degradation and it has been confirmed by OD and CFU methods. In addition, it has been proved that a close cycle water flow around UV lamp is imperative so that an appropriate dose must be delivered to microorganisms for an efficient disinfection. It has been found that due to the sensitive nature of Fluorescence spectroscopy, it yields immediate results, whereas, for CFU and OD methods, water samples needs to be inoculated for 24 h. Fluorescence spectroscopy, therefore, provide a fast, online, reliable and sensitive method for the monitoring of pathogenic quantification in drinking water. [ABSTRACT FROM AUTHOR]

In this article, approximate solutions of some PDE of fractional order are investigated with the help of a new semi-analytical method called the optimal auxiliary function method. The proposed method was tested upon the time-fractional Fisher equation, the time-fractional Fornberg-Whitham equation, and the time-fractional Inviscid Burger equation. The beauty of this method is that there is no need for discretization and assumptions of small or large parameters and provides an approximate solution after only one iteration. The numerical results obtained by the proposed method compared with the other existing methods used in the literature. From the numerical and graphical results, it is clear that the proposed method gives a better solution than existing methods. The MATHEMATICA software package has been used for the huge computational work. [ABSTRACT FROM AUTHOR]

Irregularity indices are graph-theoretic parameters designed to quantify the irregularity in a graph. In this paper, we study the practical applicability of irregularity indices in QSPR modeling of the physicochemical and quantum-theoretic properties of compounds. Our comparative testing shows that the recently introduced I R A index has significant priority in applicability over other irregularity indices. In particular, we show that the correlation potential of the I R A index with certain physicochemical and quantum-theoretic properties such as the enthalpy of formation, boiling point, and π -electron energies is significant. Our QSPR modeling suggests that the regression models with the aforementioned characteristics such as strong curve fitting are, in fact, linear. Considering this the motivation, the I R A index was studied further, and we provide analytically explicit expressions of the I R A index for certain graph operations and compositions. We conclude the paper by reporting the conclusions, implications, limitations, and future scope of the current study. [ABSTRACT FROM AUTHOR]

In the present paper, the optimal auxiliary function method (OAFM) has been extended for the first time to fractional-order partial differential equations (FPDEs) with convergence analysis. To find the accuracy of the OAFM, we consider the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations as a test example. The proposed technique has auxiliary functions and convergence control parameters, which accelerate the convergence of the method. The other advantage of this method is that there is no need for a small or large parameter assumption, and it gives an approximate solution after only one iteration. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different FPDEs. [ABSTRACT FROM AUTHOR]

In this paper, a comparative study of natural transform decomposition method and new iterative method is presented. The proposed methods are tested upon nonlinear fractional order foam drainage problem and fractional order modified regularized long-wave equation. The solutions obtained by the proposed methods have been compared with the classical solutions and the solution obtained by Adomian decomposition method. Furthermore, the efficiency and reliability of the proposed methods are shown with the help of numerical and graphical results. The fractional order derivatives are defined in Caputo's sense whose order belongs to the closed interval [0,1]. The results reveal that the methods are quickly convergent and yield encouraging results. [ABSTRACT FROM AUTHOR]

In this paper, the Optimal Homotopy Asymptotic Method is extended to derive the approximate solutions of fractional order two-dimensional partial differential equations. The fractional order Zakharov–Kuznetsov equation is solved as a test example, while the time fractional derivatives are described in the Caputo sense. The solutions of the problem are computed in the form of rapidly convergent series with easily calculable components using Mathematica. Reliability of the proposed method is given by comparison with other methods in the literature. The obtained results showed that the method is powerful and efficient for determination of solution of higher-dimensional fractional order partial differential equations. [ABSTRACT FROM AUTHOR]

An experiment having four replications was designed in Randomized complete block design with split plot arrangements (RCBD in split plot) and conducted at Research Farm of Agronomy, The University of Agriculture Peshawar, during kharif 2015. Row spacing (45, 55, 65 and 75 cm) were allotted to main plots while nitrogen placement methods (control, single side of the row, between the rows and both sides of the row,) were assigned to sub plots. Maximum cob height from ground (81.1 cm), ear weight at silking (166.2 g), grain yield (2226.2 kg ha-1)and thousand grain weight (194.5 g) were obtained from row spacing of 65 cm and biological yield (15058.1 kg ha-1) was observed at row spacing of 45 cm while maximum weeds dry weight (90.5g m-2) was examined at row spacing of 75 cm. Similarly maximum cob height from ground (81.6 cm), ear weight at silking (1661.8 g), grain yield (2184.9 kg ha-1), biological yield (14821.9 kg ha-1) and thousand grain weight (199 g) were obtained from applying nitrogen to both sides of the row while maximum weeds dry weight (79.2 g) was noted in control plots. All the interactions (RS×NP) were found non-significant for all the parameters. It is concluded that maize should be sown at 65 cm row spacing with nitrogen applied to both sides of the rows to get maximum yield in Peshawar, Pakistan. [ABSTRACT FROM AUTHOR]

The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated. [ABSTRACT FROM AUTHOR]