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The KdV–mKdV equation is investigated in this study. This equation is a useful tool to model many nonlinear phenomena in the fields of fluid dynamics, quantum mechanics, and soliton wave theory. The exact soliton solutions of the KdV–mKdV equation are extracted using three distinct exact methods, namely, the generalized projective Riccati equation method, the modified auxiliary equation method, and the generalized unified method. Many novel soliton solutions, including kink, periodic, bright, dark, and singular dark–bright soliton solutions, are obtained. Rational functions, exponential functions, trigonometric functions, and hyperbolic functions are contained in the acquired nontrivial exact solutions. The graphical simulation of some obtained solutions is depicted using 3D plots, 2D contour plots, density plots, and 2D line plots. For the first time, the KdV–mKdV equation is investigated using the proposed three exact methods, and many novel solutions, such as dark, bright, and dark–bright singular soliton solutions, are determined, which have never been reported in the literature.

The internal atmospheric waves are gravity waves and occur in the inner part of the fluid system. In this study, a time-fractional model for internal atmospheric waves is investigated with the Caputo-Fabrizio time-fractional differential operator. The analytical solution of the considered model is retrieved by the Elzaki Adomian decomposition method. The variation in the solution is examined for increasing order of the fractional parameter α through numerical and graphical simulations. The accuracy of the obtained results is established by comparing the obtained solution of considered fractional model with the results available in the literature. [ABSTRACT FROM AUTHOR]

In this article, Elzaki decomposition method (EDM) has been applied to approximate the analytical solution of the time-fractional gas-dynamics equation. The time-fractional derivative is used in the Caputo-Fabrizio sense. The proposed method is implemented on homogenous and non-homogenous cases of the time-fractional gas-dynamics equation. A comparison between the exact and approximate solutions is also provided to show the validity and accuracy of the technique. A graphical representation of all the retrieved solutions is shown for different values of the fractional parameter. The time development of all solutions is also represented in 2D graphs. The obtained results may help understand the physical systems governed by the gas-dynamics equation. [ABSTRACT FROM AUTHOR]

To analyze and study the behaviour of the shallow water waves, the perturbed Boussinesq equation has acquired fundamental importance. The principal objective of this paper is to manifest the exact traveling wave solution of the perturbed Boussinesq equation by two well known techniques named as, two variables (G′G,1G) expansion method and generalized projective Riccati equations method. A diverse array of soliton solutions, encompassing periodic, bright solitons, singular solitons and bright singular solitons are obtained by the applications of proposed techniques. The constraint conditions for newly constructed solutions are also specified. To enhance comprehension, the numerical illustrations of constructed solutions have been represented using surface plots, 2D plots and density plots. The results delineated in this paper transcend existing analysis, offering a novel, well-structured, and modern perspective. The solutions obtained not only enrich understanding of shallow water wave models but also exhibit efficacy in providing detailed descriptions of their dynamics. [ABSTRACT FROM AUTHOR]

This manuscript aims to investigate the velocity profile for the blood flow through an artery subject to magnetic field. It has been investigated how periodic acceleration of the body and slip conditions affect the irregular pulsatile blood flow across a porous media inside an artery if a magnetic field is present, under the assumption that blood is an incompressible electrically conducting fluid. A mathematical formulation involving Caputo fractional derivative serves as the basis of study. An analytical solution for fluid velocity is developed with the help of finite Hankel and Laplace transforms. The influence of fractional order on the fluid velocity is illustrated with the help of graphical simulations. The obtained results will be helpful in future research for the treatment of stenosis and other cardiovascular diseases. [ABSTRACT FROM AUTHOR]

In this article, we have studied the convergence properties of double Sumudu transformation, and we presented the results in the form of theorems on convergence, absolute convergence, and uniform convergence of Double Sumudu transformation. The Double Sumudu transform of double Integral has also been discussed for integral evaluation. Finally, we have solved a Volterra integro-partial differential equation by using Double Sumudu transformation. [ABSTRACT FROM AUTHOR]

In this study the fish scales a waste product from the fish industry were converted into water soluble protein hydrolysates on heating with aqueous solution of sodium hydroxide. Those protein hydrolysates were fractionated into different fractions using solvent extraction procedure and were also checked for their antibacterial activity using agar well diffusion method. Their antibacterial activity was also tested against six pathogenic bacteria including Escherichia coli, Margenella morganii, Haemophilus influenzae, Klebsilla pneumoniae, Pseudomonas aeruginosa, and Actenobactor baumannii. All fractions were found active against these bacteria. Their zones of inhibitions were found to vary according to the nature of solvent fraction and bacteria. Maximum zones were observed for ethyl acetate fraction (neutral) against Escherichia coli and Actenobactor baumannii with zone of inhibition 19.5 mm and 17.0 mm, respectively almost equal to the control. Their chemical composition was also analyzed by using FTIR spectroscopy and spot test. These fractions and crude were found containing amides, amino acids, amines, phenols, alcohols and aldehydes functional groups. Their antibacterial activity was then correlated with their chemical composition along with their determination for percent yield and percentage of extraction. [ABSTRACT FROM AUTHOR]

The notion of BCK-modules was introduced in [1]. In this paper we establish certain isomorphism theorems of BCK-modules and lay out its applications to the chains of BCK-modules. Moreover, exact sequences of BCK-modules are studied. [ABSTRACT FROM AUTHOR]

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