SOLITARY WAVE SOLUTIONS FOR SPACE-TIME FRACTIONAL COUPLED INTEGRABLE DISPERSIONLESS SYSTEM VIA GENERALIZED KUDRYASHOV METHOD

In this article, space-time fractional coupled integrable dispersionless system is considered, and we use fractional derivative in the sense of modified Riemann-Liouville. The fractional system has reduced to an ordinary differential system by fractional transformation and the generalized Kudryashov method is applied to obtain exact solutions. We also testify performance as well as precision of the applied method by means of numerical tests for obtaining solutions. The obtained results have been graphically presented to show the properties of the solutions

Homotopy perturbation method-based soliton solutions of the time-fractional (2+1)-dimensional Wu–Zhang system describing long dispersive gravity water waves in the ocean

Physical phenomena and natural disasters, such as tsunamis and floods, are caused due to dispersive water waves and shallow waves caused by earthquakes. In order to analyze and minimize damaging effects of such situations, mathematical models are presented by different researchers. The Wu–Zhang (WZ) system is one such model that describes long dispersive waves. In this regard, the current study focuses on a non-linear (2 + 1)-dimensional time-fractional Wu–Zhang (WZ) system due to its importance in capturing long dispersive gravity water waves in the ocean. A Caputo fractional derivative in the WZ system is considered in this study. For solution purposes, modification of the homotopy perturbation method (HPM) along with the Laplace transform is used to provide improved results in terms of accuracy. For validity and convergence, obtained results are compared with the fractional differential transform method (FDTM), modified variational iteration method (mVIM), and modified Adomian decomposition method (mADM). Analysis of results indicates the effectiveness of the proposed methodology. Furthermore, the effect of fractional parameters on the given model is analyzed numerically and graphically at both integral and fractional orders. Moreover, Caputo, Caputo–Fabrizio, and Atangana–Baleanu approaches of fractional derivatives are applied and compared graphically in the current study. Analysis affirms that the proposed algorithm is a reliable tool and can be used in higher dimensional fractional systems in science and engineering

Exploring Aspects Of Design And Safety Of Children Playgrounds In Malaysia

Taman permainan merupakan sebuah tempat untuk kanak-kanak membina pengalaman serta memperoleh keseronokan bermain di persekitaran luar. Ia dapat membantu meningkatkan kompetensi fizikal dan pengurusan emosi kanak-kanak A playground is a place to give children some excitement of outdoor playfulness and provides essential childhood experiences. It helps in developing their physical and emotional competencie

SOLVING BURGER’S AND COUPLED BURGER’S EQUATIONS WITH CAPUTO-FABRIZIO FRACTIONAL OPERATOR

In this paper, we apply Daftardar-Jafari method (DJM) to obtain approximate solutions of the nonlinear Burgers (NBE) and coupled nonlinear Burger’s equations (CNBEs) with Caputo-Fabrizio fractional operator (CFFO). The efficiency of the considered method is illustrated by some examples. Graphical results are utilized and discussed quantitatively to illustrate the solution. The results reveal that the suggested algorithm is very effective and simple and can be applied for other problems in sciences and engineering

Role of dietary fiber and lifestyle modification in gut health and sleep quality

Dietary fiber has an immense role in the gut microbiome by modulating juvenile growth, immune system maturation, glucose, and lipid metabolism. Lifestyle changes might disrupt gut microbiota symbiosis, leading to various chronic diseases with underlying inflammatory conditions, obesity, and its associated pathologies. An interventional study of 16 weeks examined the impact of psyllium husk fiber with and without lifestyle modification on gut health and sleep quality in people with central obesity (men = 60 and women = 60), those aged from 40 to 60 years, those having WC ≥ 90 cm (men) and WC ≥ 80 cm (women), and no history of any chronic disease or regular medication. The participants were subgrouped into three intervention groups, namely, the psyllium husk fiber (PSH) group, the lifestyle modification (LSM) group, and the LSM&PSH group and control group with equal gender bifurcation (men = 15 and women = 15). A 24-h dietary recall, gastrointestinal tract (GIT) symptoms, and sleep quality analysis data were collected on validated questionnaires. The analyses of variance and covariance were used for baseline and post-intervention, respectively. Student's t-test was applied for pre- and post-intervention changes on the variable of interest. The intervention effect on GIT health was highly significant (P < 0.001). The mean GIT scores of the LSM, PSH, and LSM&PSH groups were 2.99 ± 0.14, 2.49 ± 0.14, and 2.71 ± 0.14, respectively, compared to the mean GIT scores of the control group. No significant (P = 0.205) effect of either intervention was observed on sleep quality. The study concluded that psyllium husk fiber significantly improved the GIT symptoms, while no significant effect of the intervention was observed on sleep quality analysis

HYPERBOLIC TYPE SOLUTIONS FOR THE COUPLE BOITI-LEON-PEMPINELLI SYSTEM

In this paper, the (1/G')-expansion method is used to solve the coupled Boiti-Leon-Pempinelli (CBLP) system. The proposed method was used to construct hyperbolic type solutions of the nonlinear evolution equations. To asses the applicability and effectiveness of this method, some nonlinear evolution equations have been investigated in this study. It is shown that with the help of symbolic computation, the (1/G')-expansion method provides a powerful and straightforward mathematical tool for solving nonlinear partial differential equations

Abundant optical soliton solutions for an integrable (2+1)-dimensional nonlinear conformable Schrödinger system

Abstract The analytical solutions of the integrable generalized ( 2 + 1 ) -dimensional nonlinear conformable Schrodinger (NLCS) system of equations was explored in this paper with the aid of three novel techniques which consist of ( G ′ / G ) -expansion method, generalized Riccati equation mapping method and the Kudryashov method in the conformable sense. We have discovered a new and more general variety of exact traveling wave solutions by using the proposed methods with a variety of soliton solutions of several structures. With several plots illustrating the behavior of dynamic shapes of the solutions, the findings are highly applicable and detailed the physical dynamic of the considered nonlinear system

Hyperbolic type harmonically convex function and integral inequalities

In this paper, we define a new class of harmonic convexity i.e. Hyperbolic type harmonic convexity and explore its algebraic properties. Employing this new definition, some integral inequalities of Hermite-Hadamard type are presented. Furthermore, we have presented Hermite-Hadamard inequality involving Riemann Liouville fractional integral operator. We believe the ideas and techniques of this paper may inspire further research in various branches of pure and applied sciences.Publisher's Versio

The fractal-fractional Atangana-Baleanu operator for pneumonia disease: stability, statistical and numerical analyses

The present paper studies pneumonia transmission dynamics by using fractal-fractional operators in the Atangana-Baleanu sense. Our model predicts pneumonia transmission dynamically. Our goal is to generalize five ODEs of the first order under the assumption of five unknowns (susceptible, vaccinated, carriers, infected, and recovered). The Atangana-Baleanu operator is used in addition to analysing existence, uniqueness, and non-negativity of solutions, local and global stability, Hyers-Ulam stability, and sensitivity analysis. As long as the basic reproduction number $\mathscr{R}_{0}$ is less than one, the free equilibrium point is local, asymptotic, or otherwise global. Our sensitivity statistical analysis shows that $\mathscr{R}_{0}$ is most sensitive to pneumonia disease density. Further, we compute a numerical solution for the model by using fractal-fractional. Graphs of the results are presented for demonstration of our proposed method. The results of the Atangana-Baleanu fractal-fractional scheme is in excellent agreement with the actual data

Thermo-viscoelastic orthotropic constraint cylindrical cavity with variable thermal properties heated by laser pulse via the MGT thermoelasticity model

Abstract In the past few decades, many models have been proposed to address the shortcomings found in the classical theories of thermoelasticity and to allow limited speeds of heat waves. In this context, in the current paper a new generalized model of thermoelasticity based on the Moore–Gibson–Thompson (MGT) equation has been introduced. This new model can be derived by introducing the relaxation time factor into the third type of Green–Naghdi model (GN-III). In contrast to the previous works, it was taken into account that the physical properties of the material are dependent on temperature and on the viscous type. The viscoelastic medium has been assumed to obey the Kelvin–Voigt model. On the basis of the present model, thermo-viscoelastic interactions have been investigated in an unbounded orthotropic body with a cylindrical cavity. The surface of the cavity is restricted and exposed to a pulse-formed heat flow that dissolves exponentially. The characteristic thermal modulus of the material is assumed to be a linear function of temperature. The Laplace transform can be used to eliminate time dependency from control equations. Using a suitable approximate method, the transformed equations have been finally inverted by numerical inversion of the Laplace transform. Certain comparisons have been introduced to estimate the effects of the viscosity, pulsed heat, and thermal temperature-independent properties on all studied fields. A comparison with previous models of thermoelasticity is also performed in tables to verify the accuracy of the proposed model. We found from the results that the physical fields strongly depend on the viscoelastic parameter, the change of the thermal conductivity, and pulsed heat, so it is not possible to neglect their effect on the manufacturing process of machines and devices