فصلنامه مدل سازی پیشرفته ریاضی
سال دهم شماره 1 (بهار و تابستان 1399)

‎ ‎In ‎‎t‎his article, we present a ‎‎‎numerical ‎method ‎for‎ solving a class of ‎two-‎dimensional fractional optimal control problems ‎by‎ the Legendre ‎polynomial‎ basis with fractional operational ‎matrix‎. It should be mentioned that the dynamic system of the problem is based on the Caputo fractional partial derivative. This method, the dual integral is approximated by ‎Gauss-‎Legendre rule, and then by using the Lagrangian equation, a nonlinear equation is obtained. This nonlinear equation set is solved by Newton's iterative method and unknown coefficients is determined. Finally, the proposed method was applied on a fractional problem with the different degree of fractional derivative. Also, the CPU time of method is exhibited. It is notable that all calculations were obtained by the Mathematica software.

In this paper a nonlinear control method is designed to stabilize the fractional-order nonlinear chaotic systems (FONCS). The main feature of this control technique is swift convergence to the equilibrium point. Moreover, fractional version of Lyapunov stability theorem is utilized to prove the analytical results. Also, the ability of stabilization and robustness against system uncertainties are other characteristics of the proposed method. Numerical simulations are presented to emphasize the usefulness of the suggested approach in practice. It is worth to mention that the introduced nonlinear method can be used to control of almost all kind of uncertain chaotic fractional-order systems.

Often, due to conditions under which measurements are made, spatio-temporal data contain missing values. Missing data in spatial or temporal vicinity may include useful information. Using this information, we can provide more accurate results, so missing data should be carefully examined. By modeling the missing process and spatio-temporal measurement process jointly, some lost information could be recovered. In this paper, we implement joint modeling in a Bayesian framework using the "shared parameter model" technique, so that the bad effects of missing values will be moderated. Also, we will associate these two processes via a latent spatio-temporal random field. To estimate the model parameters and for predictions, the Bayesian method INLA using SPDE approach is applied. Also, the lake surface water temperature data for Caspian sea is used to evaluate the performance of the joint model.

In this paper, an efficient combination of the time-splitting and meshless local Petrov-Galerkin method for the numerical solution of Ginzburg–Landau equation in‎‏ ‎two and three dimensions is presented. ‎The main idea of splitting scheme is separating the original equation in time into two parts, linear and nonlinear‎. ‎Since, solving the nonlinear part based on the weak form is complicated and contains error, the split-step in time will be used. we solve the nonlinear part analytically and linear part numerically by the meshless local Petrov-Galerkin method in space variables and the Crank-Nicolson method in time‎. Hence, the moving Kriging interpolation is used instated of moving least squares. Therefore, the shape functions of the meshless local Petrov-Galerkin method have the Kronecker's delta property and the boundary conditions can be implemented directly and easily‎. ‎ ‎Several examples for two and three dimensions are presented and the results are compared with their analytical solutions to demonstrate the validity and capability of this method‎.

‎In this paper‎, ‎the fractional-order model for cooling of a semi-infinite body by radiation is considered‎.‎In the supposed semi-infinite body‎, ‎the equation of heat along with an initial condition and an asymptotic boundary condition form an equivalent equation in which the order of derivatives is halved‎.‎This equation and a boundary condition introduced by the radiation heat transfer give rise to an initial value problem‎, ‎whose differential equation is nonlinear and fractional order‎.‎The semi-analytical solution to this nonlinear model was determined asymptotically at small and large times‎.‎Moreover‎, ‎two numerical methods including Grunwald-Letnikov approximation and Muntz-Legendre approximation yield numerical solutions to the problem‎.

In the literature, statistical estimation of the stress-strength reliability parameter R=P(X>Y) has attracted enormous interest. Recently, Ghitany et al. [7] studied statistical estimation of the parameter R in power Lindley distribution based on complete data sets. However, in practice, we may deal with record breaking data sets in which only values larger than the current extreme value are reported. In this paper, assuming that stress and strength random variables X and Y are independently distributed as power Lindley distribution, we consider estimation of the reliability parameter R based on upper record values. First, we obtain the maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval. Then, considering squared error and Linex loss functions, we compute the Bayes estimates of R. Since, there are not closed forms for the Bayes estimates, we use Lindley method as well as a Markov Chain Monte Carlo procedure to obtain approximate Bayes estimates. In order to evaluate the performances of the proposed procedures, simulation studies are conducted. Finally, by analyzing real data sets, application of the proposed inferences using upper records is presented.

A type II progressive censoring scheme is one of the censoring methods that is important in life-testing studies. This method of censoring allows the experimenter to withdraw some of the tested units at different stages of testing. One question that arises when designing a type II progressive censoring is how we can decide to remove several units from the test at each step? Different answers can be made to answer this question by considering different criteria. In this paper, assuming the censoring scheme is a random variable from Binomial distribution, we intend to obtain the optimal parameter for the distribution of censoring scheme when the distribution is the Rayleigh distribution by considering two criteria, the cost of testing and the Mean squared prediction error in the two-sample prediction problem. To illustrate the effectiveness of the results, a simulation study and a real data example are presented with the help of MATLAB software.

In this paper, we assume that X is a BCK-algebra and y, t elements of X. We assign to these elements a set, denoted by F(y; t). We show that F(y; t) is a subalgebra of X. Then we prove that a BCK-algebra X is a Linear Commutative BCK-algebra if and only if every F(y; t) is an initial set of X. Moreover, we give a necessary and sufficient condition for F(y; t) to be an ideal. Finally, we show that the set consisting of all these sets forms a bounded distributive lattice.

‎This paper studies the usual stochastic‎, ‎star ‎and ‎‎convex transform orders of both series and parallel systems comprised of heterogeneous‎ (and dependent) components‎. ‎Sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of dependent‎‎components having multiple-outlier lomax model‎. ‎We also prove that‎, ‎without any restriction on the parameters‎, ‎the lifetime of a parallel or series systems‎‎with dependent heterogeneous components is smaller than that with dependent‎‎homogeneous components in the sense of the convex transform order‎.‎

Although TOPSIS is one of the widely used models in analyzing MCDM/MADM problems, there exists a necessary condition for its application that is the increasing or decreasing utility of the criteria. In the real world, in many cases, some of the criteria of decision making lack this property. In these cases an unrealistic assumption of the monotonic utility of the criteria is imposed to the model. However such an assumption may affect the accuracy of the results. This paper provides an extension of TOPSIS model which overcomes this limitation.

In this paper, we introduce a new integer valued bilinear modeling based on the Pegram and thinning operators. Some statistical properties of the model are discussed. The model parameters are estimated by the conditional least square and Yule-Walker methods. By a simulation, the performances of the two estimation methods are studied. Finally, the efficiency of the proposed model is investigated by applying it on two real data sets.

In this paper an analytical technique, namely the adomian decomposition method (ADM), has been applied to solve the governing equations for boundary- Layer problems in the case of a two dimensional incompressible flow. In the present work, Falkner-Skan equation for special circumstances (Blasius flow, Stagnation point flow, flow in a convergent channel, flow over a wedge) has been solved. It is found that this method can give very accurate results and also it is powerful mathematical tool that can be applied to a large class of Linear and nonlinear problems in different fields of science and engineering.