The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve

The swarm intelligence and evolutionary methods are commonly utilized by researchers in solving the difficult combinatorial and Non-Deterministic Polynomial (NP) problems. The N-Queen problem can be defined as a combinatorial problem that became intractable for the large ‘n’ values and, thereby, it is placed in the NP class of problems. In the present study, a solution is suggested for the N-Queen problem, on the basis of the Meerkat Clan Algorithm (MCA). The problem of n-Queen can be mainly defined as one of the generalized 8-Queen problem forms, for which the aim is placing 8 queens in a way that none of the queens has the ability of killing the others with the use of the standard moves of the chess queen. The Meerkat Clan environm

     The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approaches to treat these problems are required. In this work, the homotopy analysis method (HAM) is proposed. We use convergence control parameters to optimize the approximate solution. This method relay on choosing with complete freedom an auxiliary function linear operator and initial guess to generate the series solution. Moreover, the method gives a convenient way to guarantee the converge

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

    In this paper, the finite difference method is used to solve fractional hyperbolic partial differential equations, by modifying the associated explicit and implicit difference methods used to solve fractional  partial differential equation. A comparison with the exact solution is presented and the results are given in tabulated form in order to give a good comparison with the exact solution

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

In the present paper, three reliable iterative methods are given and implemented to solve the 1D, 2D and 3D Fisher’s equation. Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM) and Banach contraction method (BCM) are applied to get the exact and numerical solutions for Fisher's equations. The reliable iterative methods are characterized by many advantages, such as being free of derivatives, overcoming the difficulty arising when calculating the Adomian polynomial boundaries to deal with nonlinear terms in the Adomian decomposition method (ADM), does not request to calculate Lagrange multiplier as in the Variational iteration method (VIM) and there is no need to create a homotopy like in the Homotopy perturbation method (H

In this article, the backstepping control scheme is proposed to stabilize the fractional order Riccati matrix differential equation with retarded arguments in which the fractional derivative is presented using Caputo's definition of fractional derivative. The results are established using Mittag-Leffler stability. The fractional Lyapunov function is defined at each stage and the negativity of an overall fractional Lyapunov function is ensured by the proper selection of the control law. Numerical simulation has been used to demonstrate the effectiveness of the proposed control scheme for stabilizing such type of Riccati matrix differential equations.