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This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method's effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial. [ABSTRACT FROM AUTHOR]

This article introduces a novel methodology for tackling stochastic Itô Volterra-Fredholm integral equations through a pseudo-Spectral Galerkin method utilizing shifted Vieta-Fibonacci polynomials. The method is very efficient in solving integral and integro-differential equations, which often arise in many scientific and engineering fields. This approach is widely applicable in many domains, including signal processing, electromagnetic theory, population dynamics, finance, and related areas. By employing this method, the intricate task of solving such equations is simplified into a set of linear algebraic equations that are efficiently solvable via the Gauss elimination method for numerical solutions. The article also presents the existence, uniqueness, and stability of the solution. The convergence of the proposed method is rigorously established, ensuring its reliability. To validate its effectiveness, two numerical examples are provided. In addition to the examples, a comparison study is conducted between the orthonormal Bernoulli polynomials-based, second-kind shifted Chebyshev polyunomials-based pseudo-Spectral Galerkin approach and existing results based on improved hat functions. Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency, showcasing its applicability across various scientific and engineering domains. [ABSTRACT FROM AUTHOR]

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 paper introduces a computational spectral collocation approach utilizing orthonormal Chelyshkov polynomials to estimate solutions for both linear and nonlinear stochastic differential equations containing fractional Brownian motion characterized by the Hurst parameter H. The method employs Newton–Cotes nodes to transform these integral equations into manageable linear and nonlinear algebraic forms. The reliability of the proposed method is established through theorems on error estimation and convergence analysis. Moreover, some examples are given to demonstrate the viability, credibility, coherence, and dependability of the approach. Also, a comparative evaluation is conducted to contrast the results obtained from the suggested approach with those produced by the spectral collocation method utilizing orthonormal Bernoulli polynomials. Furthermore, a 95 % confidence interval is constructed for the error mean, revealing that the approximations maintain high accuracy. [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]

Recently, numerous demonstrative investigations on the mathematical modelling and analysis of Covid-19 have been performed. In this regard, a mathematical model is introduced to demonstrate the effects of vaccination on Covid-19. This study presents the five compartmental groups of the model, namely susceptible, infected, exposed, recovered groups, and vaccinated people. To make the model more realistic, the existing integer-order system has been modified using the Mittag–Leffler kernel. The formation of a fractional-order model shows the validity of this generalization with memory. In addition to the positivity solution, existence, uniqueness, and biologically feasible region are considered. The Ulam–Hyers stability is established through fixed-point theory and nonlinear analysis. The basic reproduction number, which means the number of people predicted to be secondarily infected among the susceptible population, is calculated. The considered model is assessed by using the Atangana–Baleanu fractional operator, and the fractional Adams–Bashforth numerical technique based on Lagrange polynomial interpolation is adopted to solve the model. Further, the error analysis of the present method has also been included. The behaviour of the solution is demonstrated through numerical simulations with the help of graphical representations. [ABSTRACT FROM AUTHOR]

The multidimensional poverty index of poverty is the most widely used method for estimating the poverty rate. It uses preassigned weights for poverty indicator that plays a critical role in determining an individual's poverty status. But the question immediately arises: how do we justify these weights of poverty indicators? In order to overcome this issue, we have formulated composite multidimensional poverty index and composite headcount ratio using principal component analysis. Further, the self-organizing maps clustering algorithm, the K-means clustering algorithm, and spatial analysis are used to determine the spatial and temporal disparity of different poverty levels. In this respect, an Indian state viz. Odisha has been considered as a case study. These methods cluster poverty data into different poverty levels by analysing the poverty indicators only. This study concluded that multidimensional poverty in the considered state is widespread and severe, requiring prompt government action. In comparison to other methods, this one is proven to be more robust, all-encompassing, and indicator-neutral. [ABSTRACT FROM AUTHOR]

A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed model. To solve the financial chaotic model with nonlocal operators, the fractional Adams–Bashforth method (ABM) is applied based on Lagrange polynomial interpolation (LPI). The existence and uniqueness of the solution of the model can be demonstrated using fixed point theory and nonlinear analysis. Further, the error analysis of the present method and Ulam–Hyers stability of the considered model have also been included. Obtained numerical simulations reveal that the model based on three different fractional derivatives shows various chaotic behaviors that may be useful in a practical sense which may not be observed in the integer case. [ABSTRACT FROM AUTHOR]

Rotavirus infection is also a major cause of death in babies and children. Rotavirus causes severe diarrhea in babies and infants in developed and underdeveloped countries. It has multiple types of transmission: human to human and human to the environment. This paper investigates the time‐fractional order rotavirus epidemic model in an uncertain environment defined in the Caputo–Fabrizio (CF) derivative sense. In the titled model, the initial conditions are considered as fuzzy numbers. A double parametric form (DPF) of fuzzy numbers has been used in the fuzzy fractional rotavirus model. A semi‐analytical approach called the homotopy perturbation Elzaki transform method (HPETM) has been employed to solve the present model with the fuzzy initial condition. In order to derive the existence and uniqueness of the solution of the model, the concept of fixed‐point theory is utilized. Various fuzzy and interval solutions have been computed by considering different values of fractional orders, fuzzy parameters, and parameters involved in the given model. [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 article, we accumulate theories and computing procedures to find eigenvalue bounds for interval matrices. Also, we have pointed out the computational complexity and applications of interval eigenvalue problems. Computing exact eigenvalue for the general interval matrices is an NP-hard problem. Various eigenvalue bounds for symmetric, non-symmetric, and complex interval matrices are included here. The article attempts to present some of the important methods proposed by various authors in one place, analyze them, and then final observations are made. In this respect, each of the methods has been addressed by taking simple example problems of interval matrices so that readers may understand the philosophy of those methods. Further, the increase of tightness of the solutions is also discussed. The interlinks of their development and gaps among them are highlighted. [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 manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots. [ABSTRACT FROM AUTHOR]

This article is dedicated to study the impact of machine intelligence (MI) methods viz. various types of Neural models for investigating dynamical systems arising in interdisciplinary areas. Different types of artificial neural network (ANN) methods, viz., recurrent neural network, functional‐link neural network, convolutional neural network, symplectic artificial neural network, genetic algorithm neural network, and so on, are addressed by different researchers to investigate these problems. Although various traditional methods have been developed by researchers to solve these dynamical problems but the existing traditional methods may sometimes be problem dependent, require repetitions of the simulations, and fail to solve nonlinearity behavior. In this regard, neural network model based methods are more general and solutions are continuous over the given domain of integration, self‐adaptive and can be used as a black box. As such, in this article, we have reviewed and analyzed different MI methods, which are applied to investigate these problems. This article is categorized under:Technologies > Computational IntelligenceTechnologies > Machine LearningApplication Areas > Science and Technology [ABSTRACT FROM AUTHOR]

The terms fractional differentiation and fractal differentiation are recently combined to form a new fractional differentiation operator. Several kernels, such as the power-law and the Mittag-Leffler function, are employed to investigate these novel operators. Both fractional-order and fractal dimensions are found in these developed operators. In the present investigation, we have applied these new operators to study certain chaotic attractors with Mittag-Leffler and power-law kernels. These chaotic models are solved using an effective numerical procedure called the Adams–Bashforth technique, based on two- and three-step Newton interpolation polynomials. In this analysis, the order of the fractional derivative is assumed to be the exponential, trigonometric, and hyperbolic forms of variables. The solutions obtained by the numerical procedure with two different kernels are portrayed in terms of chaotic plots. [ABSTRACT FROM AUTHOR]

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Much of the time, geological data are not accurately known. Instead, geoscientists work with a range of possible data. These data can have a range since they can vary spatially and temporally. In this context, we demonstrate how a well-established structural geological model of velocity profile of ductile simple shear, expressed as an equation, can be furthered by fuzzy set concept. The implementation of fuzzy set concepts in terms of fuzzification in (geo)scientific models takes into consideration the uncertainties of magnitudes of the parameters that define the model. The present study shows that the fuzzified velocity profile of a ductile simple shear zone with parallel boundaries is effectively independent of the dip of the shear zone. This article demonstrates how models of (structural) geological processes can be modelled by fuzzy set approach capable of incorporating a range of magnitudes of parameters. [ABSTRACT FROM AUTHOR]

The term fractional differentiation has recently been merged with the term fractal differentiation to create a new fractional differentiation operator. Several kernels were used to explore these new operators, including the power-law, exponential decay, and Mittag-Leffler functions. In this study, we analyze three forms of interpersonal relationships model. The numerical solution of the fractal–fractional interpersonal relationships model based on different kernels has been investigated. The new operators contain two parameters: one is for fractional order α , and the other is for fractal dimension γ. We use Lagrangian polynomial interpolation along with numerical method and the concept of fractional theory to solve these three forms of the titled model. All three forms of the numerical computation are compared with the solutions of the other existing method when α = γ = 1 that leads to a good agreement. The existence and uniqueness of the models have been studied using the Picard–Lindelöf theorem. To understand how the effects of fractal dimension and fractional order influence the model, we have illustrated various plots taking different values of α and γ. [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, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada–Kotera (SSK) and Lax's KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, α = 1 revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values α are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated. [ABSTRACT FROM AUTHOR]

The study of the time‐fractional vibration equation (VE) of large membranes is vital due to its widespread applications. Various researchers have investigated the titled problem in which the variables and parameters have been considered as crisp/exact. However, in actual practice, this may contain uncertainty because of errors in observations, maintenance induced error, and other errors. In this investigation, we have considered these uncertainties as interval/fuzzy, and a method, namely double parametric form of fuzzy numbers are used to solve the uncertain fractional vibration model of order α(1<α≤2). The titled problem has been solved under various cases using the Residual power series method (RPSM). The performance of the present method is well in terms of computational efficiency. The consistency of the method is displayed by providing numerical solutions for various cases. Obtained results are depicted in terms of figures and are also compared with individual cases. [ABSTRACT FROM AUTHOR]

The analysis of interpersonal relationships has started to become popular in the last few decades. Interpersonal relationships exist in many ways, including family, friendship, job, and clubs. In this manuscript, we have implemented the homotopy perturbation Elzaki transform method to obtain the solutions of romantic and interpersonal relationships model involving time‐fractional‐order derivatives with non‐singular kernels. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. This method offers a rapidly convergent series of solutions. The present approach explores the dynamics of love between couples. Validation and usefulness of the method are incorporated with new fractional‐order derivatives with exponential decay law and with general Mittag–Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo and newly defined fractional derivatives are discussed. [ABSTRACT FROM AUTHOR]

A widescale description of various phenomena in science and engineering such as physics, chemical, acoustics, control theory, finance, economics, mechanical engineering, civil engineering, and social sciences is well described by nonlinear fractional differential equations (NLFDEs). In turbulence, fluid dynamics, and nonlinear biological systems, applications of NLFDEs can also be found. NLFDEs are believed to be powerful tools to describe real‐world problems more precisely than the differential equation of the integer‐order. In this research, we have used the fractional reduced differential transform method (FRDTM) to find the solution of the time‐fractional Sawada‐Kotera‐Ito seventh‐order equation. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. In addition, compared to other methods, this approach needs less calculation. For special cases of an integer and noninteger orders, computed results are compared with existing results. Present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. Convergence analysis of the results has also been studied with the increasing number of terms of the solution. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a fuzzy model for the health risk challenges associated with alcoholism. The fuzziness gets into the system by assuming uncertainty condition in the measure of influence of the risky individual and the additional death rate. Specifically, the fuzzy numbers are defined functions of the degree of peer influence of a susceptible individual into drinking behavior. The fuzzy basic risk reproduction number R 0 f is computed by means of Next-Generation Matrix and analyzed. The analysis of R 0 f reveals that health risk associated with alcoholism can be effectively controlled by raising the resistance of susceptible individuals and consequently reducing their chances of initiation of drinking behavior. When perceived respectable individuals in the communities are involved in health education campaign, the public awareness about prevailing risks increases rapidly. Consequently, a large population proportion will gain protection from initiation of drinks which would accelerate their health condition into more risky states. In a situation where peer influence is low, the health risks are likely to be reduced by natural factors that provide virtual protection from alcoholism. However, when the perceived most influential people in the community engage in alcoholism behavior, it implies an increase in the force of influence, and as such, the system will be endemic. [ABSTRACT FROM AUTHOR]

Fractional Brusselator reaction‐diffusion system (BRDS) is used for modeling of specific chemical reaction‐diffusion processes. It may be noted that numerous models in nonlinear science are defined by fractional differential equations (FDEs) in which an unknown function appears under the operation of a fractional‐order derivative. Even though many researchers have studied the applicability and practicality of this model, the analytical approach of this model is rarely found in the literature. In this investigation, a novel semi‐analytical technique called fractional reduced differential transform method (FRDTM) has been applied to solve the present model, which is characterized by the time‐fractional derivative (FD). Obtained outcomes are compared with the solution of other existing methods for a particular case. Also, the convergence analysis of this model has been studied here. [ABSTRACT FROM AUTHOR]

This article deals with the solution of a fractionally-damped generalized Bagley–Torvik (BT) equation whose damping characteristics are well-defined by means of the fractional derivative (FD) of the Riemann–Liouville and the Liouville–Caputo types. The Ho-motopy Analysis Method (HAM) is implemented for computing the dynamic response (DR) analysis. Two external forces or loads (namely, the unit step function and the unit impulse function) are considered for the analysis presented here. The FD is first defined and then used here in the Riemann–Liouville sense and the Liouville–Caputo sense. In order to show the efficiency, powerfulness, and validations of the present analysis, the obtained results are compared with the solutions derived earlier by Suarez and Shokooh (1997) who used the eigenfunction expansion method and by Podlubny (1999) who used fractional-order Green's function. [ABSTRACT FROM AUTHOR]

This paper is concerned with the free vibration problem of nanobeams based on Euler-Bernoulli beam theory. The governing equations for the vibration of Euler nanobeams are considered based on Eringen's nonlocal elasticity theory. In this investigation, computationally efficient Bernstein polynomials have been used as shape functions in the Rayleigh-Ritz method. It is worth mentioning that Bernstein polynomials make the computation efficient to obtain the frequency parameters. Different classical boundary conditions are considered to address the titled problem. Convergence of frequency parameters is also tested by increasing the number of Bernstein polynomials in the simulation. Further, comparison studies of the results with existing literature are done after fixing the number of polynomials required from the said convergence study. This shows the efficacy and powerfulness of the method. The novelty of using the Bernstein polynomials is addressed in detail and solutions obtained by this method provide a better representation of the vibration behavior of Euler nanobeams. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to find the solution of time-fractional Korteweg–de-Vries (tfKdV) equations which may be used for modeling various wave phenomena using homotopy perturbation transform method (HPTM). Design/methodology/approach: HPTM, which consists of mainly two parts, the first part is the application of Laplace transform to the differential equation and the second part is finding the convergent series-type solution using homotopy perturbation method (HPM), based on He's polynomials. Findings: The study obtained the solution of tfKdV equations. An existing result "as the fractional order of KdV equation given in the first example decreases the wave bifurcates into two peaks" is confirmed with present results by HPTM. A worth mentioning point may be noted from the results is that the number of terms required for acquiring the convergent solution may not be the same for different time-fractional orders. Originality/value: Although third-order tfKdV and mKdV equations have already been solved by ADM and HPM, respectively, the fifth-order tfKdV equation has not been solved yet. Accordingly, here HPTM is applied to two tfKdV equations of order three and five which are used for modeling various wave phenomena. The results of third-order KdV and KdV equations are compared with existing results. [ABSTRACT FROM AUTHOR]

Risk and uncertainties plays a major role in stock market investments. It is a pedagogical practice to deduce probability distributions for analysing stock market returns using theoretical models of investor behaviour. Generally, economists estimate probability distributions for stock market returns that are observed from the history of past returns. Besides this, there are impreciseness involved in various factors affecting market investment and returns. As such, we need to model a more reliable strategy that will quantify the uncertainty with better confidence. Here, we have presented a computational method to solve fuzzy stochastic Volterra–Fredholm integral equation which is based on the block pulse functions (BPFs) using fuzzy stochastic operational matrix (SOM). The concept of fuzziness has been hybridized with BPFs, and the corresponding stochastic integral equation has been modelled. For illustration, the developed model has been used to investigate an example problem of Black–Scholes fuzzy stochastic differential equation (FSDE), and the results are compared in special cases. [ABSTRACT FROM AUTHOR]

Purpose In structural mechanics, systems with damping factor get converted to nonlinear eigenvalue problems (NEPs), namely, quadratic eigenvalue problems. Generally, the parameters of NEPs are considered as crisp values but because of errors in measurement, observation or maintenance-induced errors, the parameters may have uncertain bounds of values, and such uncertain bounds may be considered in terms of closed intervals. As such, this paper aims to deal with solving nonlinear interval eigenvalue problems (NIEPs) with respect to damped spring-mass systems having interval parameters.Design/methodology/approach Two methods, namely, linear sufficient regularity perturbation (LSRP) and direct sufficient regularity perturbation (DSRP), have been proposed for solving NIEPs based on sufficient regularity perturbation method for intervals. LSRP may be used for solving NIEPs by linearizing the eigenvalue problems into generalized interval eigenvalue problems, and DSRP may be considered as a direct solution procedure for solving NIEPs.Findings LSRP and DSRP methods help in computing the lower and upper eigenvalue and eigenvector bounds for NIEPs which contain the crisp eigenvalues. Further, the DSRP method is computationally efficient compared to LSRP.Originality/value The efficiency of the proposed methods has been validated by example problems of NIEPs. Moreover, the procedures may be extended for other nonlinear interval eigenvalue application problems. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval shallow water wave equations have been solved by homotopy perturbation method (HPM). In this study, basin depth and initial conditions have been taken as interval and the single parametric concept has been used to handle the interval uncertainty.Design/methodology/approach HPM has been used to solve interval shallow water wave equation with the help of single parametric concept.Findings Previously, few authors found solution of shallow water wave equations with crisp basin depth and initial conditions. But, in actual sense, the basin depth, as well as initial conditions, may not be found in crisp form. As such, here these are considered as uncertain in term of intervals. Hence, interval linear and non-linear shallow water wave equations are solved in this study using single parametric concept-based HPM.Originality/value As mentioned above, uncertainty is must in the above-titled problems due to the various parametrics involved in the governing differential equations. These uncertain parametric values may be considered as interval. To the best of the authors’ knowledge, no work has been reported on the solution of uncertain shallow water wave equations. But when the interval uncertainty is involved in the above differential equation, then direct methods are not available. Accordingly, single parametric concept-based HPM has been applied in this study to handle the said problems. [ABSTRACT FROM AUTHOR]

This paper proposes the application of functional link neural networks (FLNNs) for structural response prediction of tall buildings due to seismic loads. The ground acceleration data are taken as input, and structural responses of different floors of multistorey shear buildings are considered as output. It is worth mentioning that handling of large earthquake data has become a great challenge in the design of tall structures viz., that of shear buildings. As such, here, a functional expansion block in FLNN has been used along with efficient Chebyshev and Legendre polynomials. Training is done with one earthquake data set, and testing is done with different intensities of other earthquake data sets; and it is seen that FLNN can very well predict the structural response of different floors of multistorey shear buildings subject to earthquake data. Results of the FLNN are compared with a multilayer neural network (MNN), and it is found that the FLNN gives better accuracy and takes less computation time compared to MNN, which shows the computational efficiency of FLNN over MNN. Numerical examples of two-, five-, and ten-storey buildings are considered, and corresponding results are presented in the form of tables and plots. [ABSTRACT FROM PUBLISHER]

Purpose Vibration of large membranes has great utility in engineering application such as in important parts of drums, pumps, microphones, telephones and other devices. So, to obtain a numerical solution of this type of problems is necessary and important. In general, in existing approaches, involved parameters and variables are defined exactly. Whereas in actual practice, it may contain uncertainty owing to error in observations, maintenance-induced error, etc. So, the main purpose of this paper is to solve this important problem numerically under fuzzy and interval uncertainty to have an uncertain solution and to study its behaviour.Design/methodology/approach In this study, the authors have considered a new approach is known as double parametric form of fuzzy number to model uncertain parameters. Along with this a semianalytical approach, i.e. variational iteration method, has been used to obtain uncertain bounds of the solution.Findings The variational iteration method has been successfully implemented along with the double parametric form of fuzzy number to find the uncertain solution of the vibration equation of a large membrane. The advantage of this approach is that the solution can be written in a power series or a compact form. Also, this method converges rapidly to obtain an accurate solution. Various cases depending on the functional value involved in the initial conditions have been studied and the behaviour has been analysed. Applying the double parametric form reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.Originality/value The vibration equation of large membranes has been solved under fuzzy and interval uncertainty. Uncertainties have been considered in the initial conditions. New approaches, i.e. variational iteration method along with the double parametric form, have been applied to solve the vibration equation of large membranes. [ABSTRACT FROM AUTHOR]