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This article investigates the traveling wave solution for a geophysical Boussinesq-type equation that models equatorial tsunami waves. The discussed structure exhibits explicit traveling wave solutions characterized by speeds surpassing the linear propagation speed and small amplitude wave near-field variables. A combination of traveling wave transformation, tanh method, extended tanh method, and a modified form of extended tanh method are implemented, leading to some new traveling wave solutions for the referred nonlinear model. Through the appropriate selection of parameters, the research employs two-dimensional, three-dimensional, and contour plots to showcase the characteristics of specific solutions. The presented visual representation serves as an efficient means to understand the nature of these solutions. This research further extends its investigation by transforming the considered equation into a planar dynamical structure. Through this transformation, all potential phase portraits of the dynamical system are thoroughly examined, utilizing the theory of bifurcation. In addition, this work investigates the modulation of instability in the governing equation using the linear stability analysis function. Importantly, all the newly derived solutions conform to the main equation when substituted into it. The obtained results demonstrate the effectiveness, conciseness, and efficiency of the applied techniques. These strategies have the potential to be useful in scrutinizing more complex models that appear in modern science and engineering. [ABSTRACT FROM AUTHOR]

This study focused on "Extension of synthetic division and its applications". The study was designed to show synthetic division and its extension and to point out the applications of synthetic division and its extension. The study found out that the concepts of polynomial and rational expressions in single variables are basic concepts to deal extension of synthetic division and its applications. Using the preliminary concepts, the concept of synthetic division is extended in this study. Also, the study found out that an extension of synthetic division is used for finding the oblique asymptote of the graph of a rational function, evaluating the integration of some rational functions, representing polynomial expression by factorial function in numerical analysis, and so on. [ABSTRACT FROM AUTHOR]

Purpose: Investigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment. Design/methodology/approach: Triangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment. Findings: LWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated. Originality/value: To deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work. [ABSTRACT FROM AUTHOR]

In this paper, a new method is proposed to solve type‐2 fuzzy linear system of equations by converting the system into three interval linear systems and one crisp linear system of equations. In this work, three possible cases of type‐2 fuzzy linear system is considered depending upon uncertainty (as type‐2 fuzzy number) in right‐hand side vector B˜$$ \tilde{B} $$, in co‐efficient matrix A˜$$ \tilde{A} $$, and both in co‐efficient matrix A˜$$ \tilde{A} $$ as well as right‐hand side vector B˜$$ \tilde{B} $$. Triangular perfect quasi type‐2 fuzzy numbers are taken to propose the new method. The main significance of the proposed method is that it uses the arithmetic of interval theory, which makes this method easier to handle. Five numerical examples are solved to show the validation of the proposed technique. Further, two application problems related to 6‐bar truss and rectangular sheet are encountered in type‐2 fuzzy environment. Comparison among the results obtained by the present method and previously achieved results is also made in this work, which shows that the results are close enough and, in some cases, better bounds for the solution are obtained. [ABSTRACT FROM AUTHOR]

In this article, the Gershgorin disk theorem in complex interval matrices is proposed for enclosing interval eigenvalues. This is a non-iterative method for finding eigenvalue bounds for both real and imaginary parts. Moreover, we are able to find gaps between the clusters of interval eigenvalues and have compared the results with the previous theorems for interval eigenvalue bounds for complex interval matrices. These results can be decisive for checking Hurwitz and Schur stability of complex interval matrices that appear in uncertain dynamical systems. Further bounds obtained from the present formulae can be considered as the initial bounds for iterative methods. [ABSTRACT FROM AUTHOR]

In this study, we consider the dynamics of the Babesiosis transmission on bovine populations and ticks. The most important role in the transmission of the parasite is the ticks from the Ixodidae family. The vector tick takes factors (merozoites in erythrocytes) from the diseased animal while sucking the blood. To model and investigate the transmissions of this parasite and address this important issue, we have considered the disease in a fractional epidemiological model. This paper, therefore, discusses the mechanisms of transmission of Babesiosis defined in the fractional derivative sense. The Caputo–Fabrizio (CF) derivative is considered to study the propagation mechanisms of Babesiosis. First, the important characteristics of the model have been presented, and then the transmission of the Babesiosis model defined in CF is discussed. The application of fixed-point theory is used to derive the concept of the qualitative properties of the mentioned model. The solution is obtained by using the Homotopy perturbation Elzaki transform method (HPETM). Numerical simulations are performed, and the effects of the arbitrary-order derivatives are investigated graphically. [ABSTRACT FROM AUTHOR]

In this paper, an interval solution has been constructed for the system of differential equations (SDEs) governing the COVID‐19 pandemic with uncertain parameters, namely, interval. The imposition of lockdown on infective has been considered as an interval parameter. As a result, the complete system of first‐order differential equations is transformed into interval form. The resulting interval system of differential equations (ISDEs) has been solved with help of the parametric concept and the Runge–Kutta method of order 4. Obtained results are compared with existing crisp results, and they are found to be in good agreement. [ABSTRACT FROM AUTHOR]