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# 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

### Summary

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

• Open Access

ARTICLE

Dynamical Analysis of Radiation and Heat Transfer on MHD Second Grade Fluid

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 689-703, 2021, DOI:10.32604/cmes.2021.014980
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
Abstract Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in a different field, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of ramped boundary conditions… More >

• Open Access

ARTICLE

Moving Least Squares Interpolation Based A-Posteriori Error Technique in Finite Element Elastic Analysis

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 167-189, 2021, DOI:10.32604/cmes.2021.014672
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
Abstract The performance of a-posteriori error methodology based on moving least squares (MLS) interpolation is explored in this paper by varying the finite element error recovery parameters, namely recovery points and field variable derivatives recovery. The MLS interpolation based recovery technique uses the weighted least squares method on top of the finite element method's field variable derivatives solution to build a continuous field variable derivatives approximation. The boundary of the node support (mesh free patch of influenced nodes within a determined distance) is taken as circular, i.e., circular support domain constructed using radial weights is considered. The field variable derivatives (stress… More >

• Open Access

ARTICLE

An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 687-698, 2021, DOI:10.32604/cmes.2021.014739
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >

• Open Access

ARTICLE

The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 993-1012, 2021, DOI:10.32604/cmes.2021.012702
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >

• Open Access

ARTICLE

A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 621-643, 2021, DOI:10.32604/cmes.2021.014407
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >

• Open Access

ARTICLE

Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 361-384, 2021, DOI:10.32604/cmes.2021.012720
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >

• Open Access

ARTICLE

Generalized Truncated Fréchet Generated Family Distributions and Their Applications

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 791-819, 2021, DOI:10.32604/cmes.2021.012169
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >

• Open Access

ARTICLE

MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 821-841, 2021, DOI:10.32604/cmes.2021.012529
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >

• Open Access

ARTICLE

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag–Leffler Function in the Kernel

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 359-378, 2021, DOI:10.32604/cmes.2021.011782
（This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
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 >