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Tarikul Islam and Armina Akter
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to…
Abstract
Purpose
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional
Design/methodology/approach
The rational fractional
Findings
Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.
Originality/value
The rational fractional
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J.I. Ramos and Carmen María García López
The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the…
Abstract
Purpose
The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.
Design/methodology/approach
An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.
Findings
The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.
Originality/value
The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.
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Abstract
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Svetlin Georgiev, Aissa Boukarou, Keltoum Bouhali and Khaled Zennir
This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global…
Abstract
Purpose
This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.
Design/methodology/approach
This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.
Findings
This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.
Originality/value
This article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.
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Wassim Ben Ayed and Rim Ben Hassen
This research aims to evaluate the accuracy of several Value-at-Risk (VaR) approaches for determining the Minimum Capital Requirement (MCR) for Islamic stock markets during the…
Abstract
Purpose
This research aims to evaluate the accuracy of several Value-at-Risk (VaR) approaches for determining the Minimum Capital Requirement (MCR) for Islamic stock markets during the pandemic health crisis.
Design/methodology/approach
This research evaluates the performance of numerous VaR models for computing the MCR for market risk in compliance with the Basel II and Basel II.5 guidelines for ten Islamic indices. Five models were applied—namely the RiskMetrics, Generalized Autoregressive Conditional Heteroskedasticity, denoted (GARCH), fractional integrated GARCH, denoted (FIGARCH), and SPLINE-GARCH approaches—under three innovations (normal (N), Student (St) and skewed-Student (Sk-t) and the extreme value theory (EVT).
Findings
The main findings of this empirical study reveal that (1) extreme value theory performs better for most indices during the market crisis and (2) VaR models under a normal distribution provide quite poor performance than models with fat-tailed innovations in terms of risk estimation.
Research limitations/implications
Since the world is now undergoing the third wave of the COVID-19 pandemic, this study will not be able to assess performance of VaR models during the fourth wave of COVID-19.
Practical implications
The results suggest that the Islamic Financial Services Board (IFSB) should enhance market discipline mechanisms, while central banks and national authorities should harmonize their regulatory frameworks in line with Basel/IFSB reform agenda.
Originality/value
Previous studies focused on evaluating market risk models using non-Islamic indexes. However, this research uses the Islamic indexes to analyze the VaR forecasting models. Besides, they tested the accuracy of VaR models based on traditional GARCH models, whereas the authors introduce the Spline GARCH developed by Engle and Rangel (2008). Finally, most studies have focus on the period of 2007–2008 financial crisis, while the authors investigate the issue of market risk quantification for several Islamic market equity during the sanitary crisis of COVID-19.
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Germana Giombini, Francesca Grassetti and Edgar Sanchez Carrera
The authors analyse a growth model to explain how economic fluctuations are primarily driven by productive capacities (i.e. capacity utilization driven by innovations and…
Abstract
Purpose
The authors analyse a growth model to explain how economic fluctuations are primarily driven by productive capacities (i.e. capacity utilization driven by innovations and know-how) and productive inefficiencies.
Design/methodology/approach
This study’s methodology consists of the combination of the economic growth model, à la Solow–Swan, with a sigmoidal production function (in capital), which may explain growth, poverty traps or fluctuations depending on the relative levels of inefficiencies, productive capacities or lack of know-how.
Findings
The authors show that economies may experience economic growth, poverty traps and/or fluctuations (i.e. cycles). Economic growth is reached when an economy experiences both a low level of inefficiencies and a high level of productive capacities while an economy falls into a poverty trap when there is a high level of inefficiencies in production. Instead, the economy gets in cycles when there is a large level of the lack of know-how and low levels of productive capacity.
Originality/value
The authors conclude that more capital per capita (greater savings and investment) and greater productive capacity (with less lack of know-how) are the economic policy keys for an economy being on the path of sustained economic growth.
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