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In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).
Abstract
Purpose
In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).
Design/methodology/approach
The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).
Findings
The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.
Originality/value
The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.
Details
Keywords
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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Keywords
Jihad Maulana Akbar and De Rosal Ignatius Moses Setiadi
Current technology makes it easy for humans to take an image and convert it to digital content, but sometimes there is additional noise in the image so it looks damaged. The…
Abstract
Current technology makes it easy for humans to take an image and convert it to digital content, but sometimes there is additional noise in the image so it looks damaged. The damage that often occurs, like blurring and excessive noise in digital images, can certainly affect the meaning and quality of the image. Image restoration is a process used to restore the image to its original state before the image damage occurs. In this research, we proposed an image restoration method by combining Wavelet transformation and Akamatsu transformation. Based on previous research Akamatsu's transformation only works well on blurred images. In order not to focus solely on blurry images, Akamatsu's transformation will be applied based on Wavelet transformations on high-low (HL), low-high (LH), and high-high (HH) subunits. The result of the proposed method will be comparable with the previous methods. PSNR is used as a measure of image quality restoration. Based on the results the proposed method can improve the quality of the restoration on image noise, such as Gaussian, salt and pepper, and also works well on blurred images. The average increase is around 2 dB based on the PSNR calculation.
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F.J. Farsana, V.R. Devi and K. Gopakumar
This paper introduces an audio encryption algorithm based on permutation of audio samples using discrete modified Henon map followed by substitution operation with keystream…
Abstract
This paper introduces an audio encryption algorithm based on permutation of audio samples using discrete modified Henon map followed by substitution operation with keystream generated from the modified Lorenz-Hyperchaotic system. In this work, the audio file is initially compressed by Fast Walsh Hadamard Transform (FWHT) for removing the residual intelligibility in the transform domain. The resulting file is then encrypted in two phases. In the first phase permutation operation is carried out using modified discrete Henon map to weaken the correlation between adjacent samples. In the second phase it utilizes modified-Lorenz hyperchaotic system for substitution operation to fill the silent periods within the speech conversation. Dynamic keystream generation mechanism is also introduced to enhance the correlation between plaintext and encrypted text. Various quality metrics analysis such as correlation, signal to noise ratio (SNR), differential attacks, spectral entropy, histogram analysis, keyspace and key sensitivity are carried out to evaluate the quality of the proposed algorithm. The simulation results and numerical analyses demonstrate that the proposed algorithm has excellent security performance and robust against various cryptographic attacks.
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Mushtaq Ali, Mohammed Almoaeet and Basim Karim Albuohimad
This study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them…
Abstract
Purpose
This study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented.
Design/methodology/approach
In this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox.
Findings
Applying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations.
Originality/value
This paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain.
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Keywords
This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and…
Abstract
Purpose
This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.
Design/methodology/approach
The functional analysis method is the a priori estimate method or energy inequality method.
Findings
The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.
Research limitations/implications
The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.
Originality/value
The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.
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Leandro Pinheiro Vieira and Rafael Mesquita Pereira
This study aims to investigate the effect of smoking on the income of workers in the Brazilian labor market.
Abstract
Purpose
This study aims to investigate the effect of smoking on the income of workers in the Brazilian labor market.
Design/methodology/approach
Using data from the 2019 National Health Survey (PNS), we initially address the sample selection bias concerning labor market participation by using the Heckman (1979) method. Subsequently, the decomposition of income between smokers and nonsmokers is analyzed, both on average and across the earnings distribution by employing the procedure of Firpo, Fortin, and Lemieux (2009) - FFL decomposition. Ñopo (2008) technique is also used to obtain more robust estimates.
Findings
Overall, the findings indicate an income penalty for smokers in the Brazilian labor market across both the average and all quantiles of the income distribution. Notably, the most significant differentials and income penalties against smokers are observed in the lower quantiles of the distribution. Conversely, in the higher quantiles, there is a tendency toward a smaller magnitude of this gap, with limited evidence of an income penalty associated with this habit.
Research limitations/implications
This study presents an important limitation, which refers to a restriction of the PNS (2019), which does not provide information about some subjective factors that also tend to influence the levels of labor income, such as the level of effort and specific ability of each worker, whether smokers or not, something that could also, in some way, be related to some latent individual predisposition that would influence the choice of smoking.
Originality/value
The relevance of the present study is clear in identifying the heterogeneity of the income gap in favor of nonsmokers, as in the lower quantiles there was a greater magnitude of differentials against smokers and a greater incidence of unexplained penalties in the income of these workers, while in the higher quantiles, there was low magnitude of the differentials and little evidence that there is a penalty in earnings since the worker is a smoker.
Details