169 research outputs found
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
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 is less than one, the free equilibrium point is local, asymptotic, or otherwise global. Our sensitivity statistical analysis shows that 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
Qualitative behavior of a higher-order fuzzy difference equation
MakaleWOS:000956767600002In this paper, we investigate the qualitative behavior of the fuzzy difference equation
zn +1 = Azn-s/B + C Pi(s)(i=0) z(n-i)
where n is an element of N-0 = N boolean OR{0},(z(n)) is a sequence of positive fuzzy numbers, A; B; C and the initial conditions z j; j = 0; 1, ..., s are positive fuzzy numbers and s is a positive integer. Moreover, two examples are given to verify the e ffectiveness of the results obtained
Magnetic field dependent viscous fluid-flow between squeezing plates with homogeneous and heterogeneous reactions
The impacts of magnetic field dependent viscous fluid is explored between
squeezing plates in the presence of homogeneous and heterogeneous reactions.
The unsteady constitutive equations of heat and mass transfers, modified
Navier-Stokes, magnetic field and homogeneous and heterogeneous reactions
are coupled as an system of ODE. The appropriate solutions are established
for the vertical and axial induced magnetic field equations for the
transformed and momentum as well as for the MHD pressure and torque exerted
on the upper plate, and are in details. In the case of a smooth plate, the
self-similar equation with acceptable starting assumptions and auxiliary
parameters is solved by utilising a homotopy analytics method, to generate
an algorithm with fast and guaranteed convergence. By comparing homotopy
analytics method solutions with BVP4c numerical solver packaging, the
validity and correctness of the homotopy analytics method findings are
demonstrated. Magnetic Reynolds number have been shown to cause to decrease
the distribution of magnetic field, fluid temperature, axial and tangential
velocity. The magnetic field also has vertical and axial components with
increasing viscosity. The applications of the investigation include car
magneto-rheological shock absorbers, modern aircraft landing gear systems,
procedures for heating or cooling, biological sensor systems, and
bio-prothesis, etc
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