Solving fractional PDEs by using Daftardar-Jafari method

2022 ◽  
Author(s):  
Hussein Gatea Taher ◽  
Hijaz Ahmad ◽  
Jagdev Singh ◽  
Devendra Kumar ◽  
Hassan Kamil Jassim
Keyword(s):  
Fractional Pdes

scholarly journals Bilateral Output Feedback Control of Fractional PDEs with Space-Dependent Coefficients

2020 ◽  
Vol 53 (2) ◽  
pp. 3743-3748
Author(s):  
Juan Chen ◽  
Aleksei Tepljakov ◽  
Eduard Petlenkov ◽  
Bo Zhuang
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Fractional Pdes

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

Fractional sub-equation method and its applications to nonlinear fractional PDEs

2011 ◽  
Vol 375 (7) ◽  
pp. 1069-1073 ◽  
Author(s):  
Sheng Zhang ◽  
Hong-Qing Zhang
Keyword(s):  
Equation Method ◽  
Fractional Pdes

scholarly journals Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Abir Chaouk ◽  
Maher Jneid
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Fractional Pdes ◽  
Differential Transform ◽  
Computational Work ◽  
Similar Solutions

In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

scholarly journals Point-Symmetric Extension-Based Interval Shannon-Cosine Spectral Method for Fractional PDEs

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Ruyi Xing ◽  
Yanqiao Li ◽  
Qing Wang ◽  
Yangyang Wu ◽  
Shu-Li Mei
Keyword(s):  
Spectral Method ◽  
Partition Of Unity ◽  
Gabor Wavelet ◽  
The Novel ◽  
Variational Theory ◽  
Numerical Accuracy ◽  
Approximation Accuracy ◽  
Symmetric Extension ◽  
Fractional Pdes ◽  
Shannon Wavelet

The approximation accuracy of the wavelet spectral method for the fractional PDEs is sensitive to the order of the fractional derivative and the boundary condition of the PDEs. In order to overcome the shortcoming, an interval Shannon-Cosine wavelet based on the point-symmetric extension is constructed, and the corresponding spectral method on the fractional PDEs is proposed. In the research, a power function of cosine function is introduced to modulate Shannon function, which takes full advantage of the waveform of the Shannon function to ensure that many excellent properties can be satisfied such as the partition of unity, smoothness, and compact support. And the interpolative property of Shannon wavelet is held at the same time. Then, based on the point-symmetric extension and the general variational theory, an interval Shannon-Cosine wavelet is constructed. It is proved that the first derivative of the approximated function with this interval wavelet function is continuous. At last, the wavelet spectral method for the fractional PDEs is given by means of the interval Shannon-Cosine wavelet. By means of it, the condition number of the discrete matrix can be suppressed effectively. Compared with Shannon and Shannon-Gabor wavelet quasi-spectral methods, the novel scheme has stronger applicability to the shockwave appeared in the solution besides the higher numerical accuracy and efficiency.

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