The paper deals with the traveling wave cylindrical heating systems. The analysis presented is analytical and a multi-layer model using cylindrical geometry is used to obtain the theoretical results. To validate the theoretical results, a practical model is constructed, tested and the results are compared with the theoretical ones. Comparison showed that the adopted analytical method is efficient in describing the performance of such induction heating systems.

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

      The aim of this article is to present the exact analytical solution for models as system of (2+1) dimensional PDEs by using a reliable manner based on combined LA-transform with decomposition technique and the results have shown a high-precision, smooth and speed convergence to the exact solution compared with other classic methods. The suggested approach does not need any discretization of the domain or presents assumptions or neglect for a small parameter in the problem and does not need to convert the nonlinear terms into linear ones. The convergence of series solution has been shown with two illustrated examples such (2+1)D- Burger's system and (2+1)D- Boiti-Leon-Pempinelli (BLP) system.

The aim of this work is to study a modified version of the four-dimensional Lotka-Volterra model. In this model, all of the four species grow logistically. This model has at most sixteen possible equilibrium points. Five of them always exist without any restriction on the parameters of the model, while the existence of the other points is subject to the fulfillment of some necessary and sufficient conditions. Eight of the points of equilibrium are unstable and the rest are locally asymptotically stable under certain conditions, In addition, a basin of attraction found for each point that can be asymptotically locally stable. Conditions are provided to ensure that all solutions are bounded. Finally, numerical simulations are given to veri

     In this paper, the bi-criteria machine scheduling problems (BMSP) are solved, where the discussed problem is represented by the sum of completion and the sum of late work times  simultaneously. In order to solve the suggested BMSP, some metaheurisitc methods are suggested which produce good results. The suggested local search methods are simulated annulling and bees algorithm. The results of the new metaheurisitc methods are compared with the complete enumeration method, which is considered an exact method, then compared results of the heuristics with each other to obtain the most efficient method.

     In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm).  And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr