Special Issue "Role of Computer in Modelling & Solving Real-World Problems"

Submission Deadline: 01 July 2021 (closed)
Guest Editors
Dr. Hijaz Ahmad, International Telematic University Uninettuno, Italy.
Dr. Abdon Atangana, University of the Free State, South Africa.
Dr. Mahmoud Abdel-Aty, Sohag University, Egypt.
Dr. Guotao Wang, Shanxi Normal University, China.
Dr. Clemente Cesarano, International Telematic University, Italy.


When modeling real-world problems, we often have to deal with measurements of different, related and mutually dependent processes. Partial differential equations are frequently used to model several physical phenomenons, arising in applied sciences and engineering. The solutions of these PDEs are of primary importance for the determination of physical behaviour of these physical phenomenons. The exact/analytical solutions of these PDEs are ideal, but due to mathematical complications, the exact/analytical solutions are possible only for simple problems with simple boundary conditions. The exact solutions of nonlinear PDEs arised in science and engineering are not always possible or time-consuming and thus the use of approximate/numerical approaches continuously remains an important alternative for the numerical treatment of these type equations. The numerical solutions of PDEs have been of much importance for many years. in the last few years, tremendous progress has been made to this area, due to the development of computer technology. Although significant progress has been made, still the numerical methods are in the early stage of their development.


This Special Issue deals with the recent advances in computer based techniques for partial differential equations of integer order as well as fractional-order, especially in science and engineering, and will accept high-quality papers having original research results.

The purpose of this Special Issue is to unite mathematicians with physicists, engineers and other researchers, for whom differential equations are valuable research tools.

Computational mathematical techniques
Partial differential equations
Numerical simulation
Modelling real world problems
Computer based algorithms
Advances in numerical techniques

Published Papers
  • A Stochastic Flight Problem Simulation to Minimize Cost of Refuelling
  • Abstract Commercial airline companies are continuously seeking to implement strategies for minimizing costs of fuel for their flight routes as acquiring jet fuel represents a significant part of operating and managing expenses for airline activities. A nonlinear mixed binary mathematical programming model for the airline fuel task is presented to minimize the total cost of refueling in an entire flight route problem. The model is enhanced to include possible discounts in fuel prices, which are performed by adding dummy variables and some restrictive constraints, or by fitting a suitable distribution function that relates prices to purchased quantities. The obtained fuel plan… More
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  • Numerical Solutions for Heat Transfer of An Unsteady Cavity with Viscous Heating
  • Abstract The mechanism of viscous heating of a Newtonian fluid filled inside a cavity under the effect of an external applied force on the top lid is evaluated numerically in this exploration. The investigation is carried out by assuming a two-dimensional laminar in-compressible fluid flow subject to Neumann boundary conditions throughout the numerical iterations in a transient analysis. All the walls of the square cavity are perfectly insulated and the top moving lid produces a constant finite heat flux even though the fluid flow attains the steady-state condition. The objective is to examine the effects of viscous heating in the fully… More
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  • Managing Delivery of Safeguarding Substances as a Mitigation Against Outbreaks of Pandemics
  • Abstract The optimum delivery of safeguarding substances is a major part of supply chain management and a crucial issue in the mitigation against the outbreak of pandemics. A problem arises for a decision maker who wants to optimally choose a subset of candidate consumers to maximize the distributed quantities of the needed safeguarding substances within a specific time period. A nonlinear binary mathematical programming model for the problem is formulated. The decision variables are binary ones that represent whether to choose a specific consumer, and design constraints are formulated to keep track of the chosen route. To better illustrate the problem,… More
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  • Optimum Location of Field Hospitals for COVID-19: A Nonlinear Binary Metaheuristic Algorithm
  • Abstract Determining the optimum location of facilities is critical in many fields, particularly in healthcare. This study proposes the application of a suitable location model for field hospitals during the novel coronavirus 2019 (COVID-19) pandemic. The used model is the most appropriate among the three most common location models utilized to solve healthcare problems (the set covering model, the maximal covering model, and the P-median model). The proposed nonlinear binary constrained model is a slight modification of the maximal covering model with a set of nonlinear constraints. The model is used to determine the optimum location of field hospitals for COVID-19… More
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  • Transmission and Reflection of Water-Wave on a Floating Ship in Vast Oceans
  • Abstract In this paper, we study the water-wave flow under a floating body of an incident wave in a fluid. This model simulates the phenomenon of waves abording a floating ship in a vast ocean. The same model, also simulates the phenomenon of fluid-structure interaction of a large ice sheet in waves. According to this method. We divide the region of the problem into three subregions. Solutions, satisfying the equation in the fluid mass and a part of the boundary conditions in each subregion, are given. We obtain such solutions as infinite series including unknown coefficients. We consider a limited number… More
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  • On Network Designs with Coding Error Detection and Correction Application
  • Abstract The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems. Furthermore, combinatorial design theory has several applications like detecting or correcting errors in communication systems. Network (graph) designs (GDs) are introduced as a generalization of the symmetric balanced incomplete block designs (BIBDs) that are utilized directly in the above mentioned application. The networks (graphs) have been represented by vectors whose entries are the labels of the vertices related to the lengths of edges linked to it. Here, a general method is proposed and applied to construct new networks designs.… More
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  • Optimal and Memristor-Based Control of A Nonlinear Fractional Tumor-Immune Model
  • Abstract In this article, the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune. The fractional derivatives are described in the Caputo sense. The solutions derived using this method are easy and very accurate. The model is given by its signal flow diagram. Moreover, a simulation of the system by the Simulink of MATLAB is given. The disease-free equilibrium and stability of the equilibrium point are calculated. Formulation of a fractional optimal control for the cancer model is calculated. In addition, to control the system, we propose a novel modification of its model. This modification is… More
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  • An Intelligent Cluster Optimization Algorithm for Smart Body Area Networks
  • Abstract Body Area Networks (BODYNETs) or Wireless Body Area Networks (WBAN), being an important type of ad-hoc network, plays a vital role in multimedia, safety, and traffic management applications. In BODYNETs, rapid topology changes occur due to high node mobility, which affects the scalability of the network. Node clustering is one mechanism among many others, which is used to overcome this issue in BODYNETs. There are many clustering algorithms used in this domain to overcome this issue. However, these algorithms generate a large number of Cluster Heads (CHs), which results in scarce resource utilization and degraded performance. In this research, an… More
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  • A New Metaheuristic Optimization Algorithms for Brushless Direct Current Wheel Motor Design Problem
  • Abstract The Equilibrium Optimizer (EO), Grey Wolf Optimizer (GWO), and Whale Optimizer (WO) algorithms are being recently developed for engineering optimization problems. In this paper, the EO, GWO, and WO algorithms are applied individually for a brushless direct current (BLDC) design optimization problem. The EO algorithm is inspired by the models utilized to find the system’s dynamic state and equilibrium state. The GWO and WO algorithms are inspired by the hunting behavior of the wolf and the whale, respectively. The primary purpose of any optimization technique is to find the optimal configuration by maximizing motor efficiency and/or minimizing the total mass.… More
  •   Views:560       Downloads:412        Download PDF