scholarly journals The Analysis of Fractional-Order Helmholtz Equations via a Novel Approach

2021 ◽  
Author(s):  
Pongsakorn Sunthrayuth ◽  
Zeyad Al-Zhour ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Order ◽  
Present Method ◽  
Computational Cost ◽  
Analytical Techniques ◽  
Form Solution ◽  
Effective Technique ◽  
Helmholtz Equations ◽  
Inverse Transform ◽  
Novel Approach ◽  
Fractional Analysis

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

scholarly journals A Comparative Study of the Fractional-Order System of Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1786
Author(s):  
Yanmei Cui ◽  
Nehad Ali Shah ◽  
Kunju Shi ◽  
Salman Saleem ◽  
Jae Dong Chung
Keyword(s):  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Computational Cost ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Form Solution ◽  
Order System ◽  
Burgers Equations ◽  
Adomian Decomposition ◽  
Fractional Analysis

This paper is related to the fractional view analysis of coupled Burgers equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of the Caputo-operator sense. In the current methodologies, first, we applied the Elzaki transform to the targeted problem. The Adomian decomposition method and homotopy perturbation method are then implemented to obtain the series form solution. After applying the inverse transform, the desire analytical solution is achieved. The suggested procedures are verified through specific examples of the fractional Burgers couple systems. The current methods are found to be effective methods having a close resemblance with the actual solutions. The proposed techniques have less computational cost and a higher rate of convergence. The proposed techniques are, therefore, beneficial to solve other systems of fractional-order problems.

scholarly journals Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

2019 ◽  
Vol 10 (1) ◽  
pp. 122 ◽  
Author(s):  
Hassan Khan ◽  
Umar Farooq ◽  
Rasool Shah ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Form Solution ◽  
Physical Models ◽  
Fractional Partial Differential Equations ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Closed Contact

In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations.

scholarly journals An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hassan Khan ◽  
Adnan Khan ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu ◽  
Rasool Shah
Keyword(s):  
Fractional Order ◽  
Present Method ◽  
Iterative Procedure ◽  
Laplace Transformation ◽  
Small Volume ◽  
Analytical Investigation ◽  
Form Solution ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Closed Contact

In this paper, a new so-called iterative Laplace transform method is implemented to investigate the solution of certain important population models of noninteger order. The iterative procedure is combined effectively with Laplace transformation to develop the suggested methodology. The Caputo operator is applied to express the noninteger derivative of fractional order. The series form solution is obtained having components of convergent behavior toward the exact solution. For justification and verification of the present method, some illustrative examples are discussed. The closed contact is observed between the obtained and exact solutions. Moreover, the suggested method has a small volume of calculations; therefore, it can be applied to handle the solutions of various problems with fractional-order derivatives.

scholarly journals Modified Modelling for Heat Like Equations within Caputo Operator

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2002 ◽  
Author(s):  
Hassan Khan ◽  
Adnan Khan ◽  
Maysaa Al-Qurashi ◽  
Rasool Shah ◽  
Dumitru Baleanu
Keyword(s):  
Exact Solution ◽  
Present Method ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Close Contact ◽  
Form Solution ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Closed Form Solutions ◽  
Novel Approach

The present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the Iterative Laplace transform method. The proposed method provides the series form solution that has the desired rate of convergence towards the exact solution of the problems. It is observed that the suggested method provides closed-form solutions. The reliability of the method is confirmed with the help of some illustrative examples. The graphical representation has been made for both fractional and integer-order solutions. Numerical solutions that are in close contact with the exact solutions to the problems are investigated. Moreover, the sample implementation of the present method supports the importance of the method to solve other fractional-order problems in sciences and engineering.

scholarly journals An efficient approach for solution of fractional-order Helmholtz equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nehad Ali Shah ◽  
Essam R. El-Zahar ◽  
Mona D. Aljoufi ◽  
Jae Dong Chung
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Hybrid Technique ◽  
Science And Engineering ◽  
Helmholtz Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Suggested Technique ◽  
Present Technique

AbstractIn this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform method and the homotopy perturbation method are amalgamated. Three problems are solved to validate and demonstrate the efficacy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the results by other techniques. It is shown that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

scholarly journals Approximate analytical fractional view of convection–diffusion equations

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 897-905
Author(s):  
Hassan Khan ◽  
Saima Mustafa ◽  
Izaz Ali ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Variational Iteration Method ◽  
Absolute Error ◽  
Form Solution ◽  
Diffusion Equations ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Suggested Technique ◽  
First Time ◽  
Modified Variational Iteration Method

Abstract In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection–diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.

scholarly journals A NOTE ON PHASING LONG GENOMIC REGIONS USING LOCAL HAPLOTYPE PREDICTIONS

2006 ◽  
Vol 04 (03) ◽  
pp. 639-647 ◽  
Author(s):  
ELEAZAR ESKIN ◽  
RODED SHARAN ◽  
ERAN HALPERIN
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Nucleotide Polymorphisms ◽  
Single Nucleotide ◽  
Novel Approach ◽  
Maximum Likelihood Criterion ◽  
The Common ◽  
Genomic Regions ◽  
High Computational Cost ◽  
Combining Information

The common approaches for haplotype inference from genotype data are targeted toward phasing short genomic regions. Longer regions are often tackled in a heuristic manner, due to the high computational cost. Here, we describe a novel approach for phasing genotypes over long regions, which is based on combining information from local predictions on short, overlapping regions. The phasing is done in a way, which maximizes a natural maximum likelihood criterion. Among other things, this criterion takes into account the physical length between neighboring single nucleotide polymorphisms. The approach is very efficient and is applied to several large scale datasets and is shown to be successful in two recent benchmarking studies (Zaitlen et al., in press; Marchini et al., in preparation). Our method is publicly available via a webserver at .

Solvent-Loaded Microspheres for Permeability Enhancement in Heavy Crude Oil Reservoirs

2021 ◽  
Author(s):  
Cengiz Yegin ◽  
Cenk Temizel ◽  
Mustafa Akbulut
Keyword(s):  
Energy Demand ◽  
Fossil Fuels ◽  
Analytical Techniques ◽  
Recovery Factor ◽  
Low Permeability ◽  
Sand Column ◽  
Permeability Enhancement ◽  
Recovery Potential ◽  
Novel Approach ◽  
Vis Spectroscopy

ABSTRACT With their abundancy and high-quality, it is predicted that fossil fuels will remain as the main resource that will meet the global energy demand in the several upcoming decades. Developments in hydrocarbon recovery technologies, both from conventional and unconventional reservoirs, have substantially contributed to the overall production levels in recent years. However, recovery factors obtained by using the current methods are still considered to be insufficient, and the companies have been looking for new materials and methods to enhance the efficiency and amount of recovery. One of the major issues related to low recovery factors is low permeability of reservoirs. Existence of blockages in pore throats and high level of heterogeneity lowers the mobility of hydrocarbons. In this study, we discuss development of an innovative material to be used as an additive in reservoir injection fluids to remove pore blockages in order to enhance the recovery levels. This additive material is made of pressure-sensitive microspheres loaded with solvents, which can (i) easily disperse in the injection fluid and travel to the low-permeability regions, (ii) break under pressure and confinement to release solvents, and (iii) remove blockages by targeting surroundings, especially asphalt-based particles and grains. This approach relies on the breakage of microcapsules in the confined region and release of the solvents to target blockages in porous media. In other words, the developed microspheres improve permeability of reservoirs as a result of pressure- and confinement-dependent breakage and release of solvents. Preparation of these microspheres was achieved by the encapsulation of solvent (toluene) emulsions in silica-based solid shells. Structure and stability of the solvent-loaded microspheres were examined using a variety of analytical techniques including UV-vis spectroscopy, optical microscopy, scanning electron microscope (SEM) and dynamic light scattering (DLS). It was found that the prepared microspheres possessed smooth surfaces with shell thicknesses in the range of 100-150 nm. Additionally, sand column tests were performed to evaluate the recovery potential of injection fluids in presence of solvent-loaded microspheres. It was shown that the use of solvent encapsulated in microspheres doubled the recovery factor of heavy oil compared to that of free solvent dispersed in the injection fluid. Such enhancement in the recovery factor was related to the release of solvents in localized areas, i.e., confined regions, as a consequence of breakage of microspheres. This novel approach of delivering solvents to low-permeability regions provides a significant driving force to eliminate pore blockages to facilitate mobilization of hydrocarbons trapped in confined spaces.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals X-RAY CT Reconstruction by using Spatially Non Homogeneous ICD Optimization

2019 ◽  
Vol 8 (6S3) ◽  
pp. 2043-2046
Keyword(s):  
Search Algorithm ◽  
Computational Cost ◽  
Selection Criterion ◽  
Closed Form Solution ◽  
Helical Ct ◽  
Reconstruction Algorithm ◽  
Form Solution ◽  
Ct Reconstruction ◽  
Practical Applications ◽  
Voxel Selection

Recent applications of conventional iterative coordinate descent (ICD) algorithms to multislice helical CT reconstructions have shown that conventional ICD can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts. However, high computational cost and long reconstruction times remain as a barrier to the use of conventional algorithm in the practical applications. Among the various iterative methods that have been studied for conventional, ICD has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization. The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed. The NH-ICD algorithm has a mechanism that adaptively selects voxels for update. First, a voxel selection criterion VSC determines the voxels in greatest need of update. Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence. In order to speed up each voxel update, we also propose a fast 3-D optimization algorithm that uses a quadratic substitute function to upper bound the local 3-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm. The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries.

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