Special Issue "Modeling Real World Problems with Mathematics"

Submission Deadline: 31 January 2021 (closed)
Guest Editors
Prof. Abdon Atangana, University of the Free State, South Africa
Prof. Jose Francisco Gomez Aguilar, Centro Nacional de Investigación y Desarrollo Tecnológico, México
Prof. Thabet Abdeljawad, Prince Sultan University, Saudi Arabia


One of the greatest assignment by humankind is perhaps to control the environment within which they leave. In other to achieve their goal, they have to observe, analyse and predict. the two last steps are very important and can only be achieved via modeling. This requires first a clear conversion of observed fact into mathematical models. The mathematical models are then used for further analysis. In particular, one needs to find exact or approximate solutions to predict the future behavior of such observed facts. In the last decades, many techniques have been suggested to help modeling real world problems in all field of science, technology and engineering. On the other hand new analytical methods have been suggested in order to provide exact solutions to real world problems, nevertheless there exist in nature many real world problems that could not be solved using analytical methods. To handle these problems, researchers will rely on numerical methods. 


The special issue will be devoted to collecting novel results including but not limited to:

1) Modeling the dynamic spread of corona virus

2) modeling social real world problems

2) New numerical methods for ordinary differential equations and application 

3) Modeling with delay differential equations

4) Modeling with stochastic differential equations 

5) Modeling real world with partial differential equations

6) Fractional and fractal differentiation with applications

Published Papers
  • An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions
  • Abstract Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions. The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations. This is fulfilled by considering time variable as normal space variable. Under this scheme, there is no need to remove time-dependent variable during the whole solution process. Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method. We propose a simple shifted domain method, which can avoid the full-coefficient interpolation matrix easily. Numerical experiments performed with… More
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  • The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles
  • Abstract

    In this paper, the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles. When considering solving sloshing problems with baffles by using boundary integral methods, degenerate geometry and problems of numerical instability are inevitable. To avoid numerical instability, the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance. Again, the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme. A weighting factor of the group-preserving scheme is introduced into a linear system… More

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  • A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data
  • Abstract In this paper, a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied. The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method. It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions. The new shape parameter increases the flexibility of the statistical properties of the traditional inverse Lomax distribution including mean, variance, skewness and kurtosis. The moments, entropies, order statistics and other properties are discussed. Six methods of estimation are… More
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  • Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation
  • Abstract This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes… More
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  • Generalized Truncated Fréchet Generated Family Distributions and Their Applications
  • Abstract Understanding a phenomenon from observed data requires contextual and efficient statistical models. Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations. Modern examples include the distributions of the truncated Fréchet generated family. In this paper, we go even further by introducing a more general family, based on a truncated version of the generalized Fréchet distribution. This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters, as well as the skewness and weight of the tails. We also investigate the main functions of the new… More
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  • MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators
  • Abstract The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic (MHD) time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress, energy, and velocity profile. Recently, new fractional differential operators are used to define ramped temperature and ramped velocity. The obtained analytical solutions are plotted for different values of emerging parameters. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics… More
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  • New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag–Leffler Function in the Kernel
  • Abstract In the present case, we propose the novel generalized fractional integral operator describing Mittag–Leffler function in their kernel with respect to another function Ф. The proposed technique is to use graceful amalgamations of the Riemann–Liouville (RL) fractional integral operator and several other fractional operators. Meanwhile, several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n (n ∈ N) for the proposed fractional operator. In order to confirm and demonstrate the proficiency of the characterized strategy, we analyze existing fractional integral operators in terms of classical fractional order. Meanwhile, some special cases are… More
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