Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2022.5768
Saba Abdul-Wahed, M. K. Hussein, H. Ahmed
Digital compression of images is a topic that has appeared in a lot of studies over the past decade to this day. As wavelet transform algorithms advance and procedures of quantization have helped to bypass current compression of image standards such as the JPEG algorithm. To get the highest effectiveness in compression of image transforms of wavelet need filters which gather a desirable character's number i.e., symmetry and orthogonally. Nevertheless, wave design capabilities are restricted due to their ability to have all of such desirable characters at the same time. The multi-wavelet technology removes a few of the restrictions of the wavelet play more than the options of design and thus able to gather all desired Characters of transforming. Wavelet andmulti-wave filter banks are tested on a larger scale with images, providing more useful analysis. Multiple waves indicate energy-compression efficiency (a higher compression ratio usually indicates a higher mean square error, MSE, in the compressed image). Filter bank Characters such as orthogonal and compact support, symmetry, and phase response are important factors that also affect MSE and professed quality of the image. The current work analyzes the multi-wave Characters effect on the performance of compression of images. Four multi-wavelength Characters (GHM, CL, ORT4) were used in this thesis and the compression of image performance of grayscale images was compared with common scalar waves (D4). SPIHT quantification device in stress chart and use of PSNR and subjective quality measures to assess performance. The results in this paper point out those multi wave characteristics that are most important for the compression of images. Moreover, PSNR results and subjective quality show similar performance to the best scalar and multi-waves. The analysis also shows that a programmer based on multi-band conversion significantly improves the perceived image quality.
{"title":"Compression of image using multi-wavelet techniques","authors":"Saba Abdul-Wahed, M. K. Hussein, H. Ahmed","doi":"10.22075/IJNAA.2022.5768","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5768","url":null,"abstract":"Digital compression of images is a topic that has appeared in a lot of studies over the past decade to this day. As wavelet transform algorithms advance and procedures of quantization have helped to bypass current compression of image standards such as the JPEG algorithm. To get the highest effectiveness in compression of image transforms of wavelet need filters which gather a desirable character's number i.e., symmetry and orthogonally. Nevertheless, wave design capabilities are restricted due to their ability to have all of such desirable characters at the same time. The multi-wavelet technology removes a few of the restrictions of the wavelet play more than the options of design and thus able to gather all desired Characters of transforming. Wavelet andmulti-wave filter banks are tested on a larger scale with images, providing more useful analysis. Multiple waves indicate energy-compression efficiency (a higher compression ratio usually indicates a higher mean square error, MSE, in the compressed image). Filter bank Characters such as orthogonal and compact support, symmetry, and phase response are important factors that also affect MSE and professed quality of the image. The current work analyzes the multi-wave Characters effect on the performance of compression of images. Four multi-wavelength Characters (GHM, CL, ORT4) were used in this thesis and the compression of image performance of grayscale images was compared with common scalar waves (D4). SPIHT quantification device in stress chart and use of PSNR and subjective quality measures to assess performance. The results in this paper point out those multi wave characteristics that are most important for the compression of images. Moreover, PSNR results and subjective quality show similar performance to the best scalar and multi-waves. The analysis also shows that a programmer based on multi-band conversion significantly improves the perceived image quality.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1519-1535"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68127839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2022.5771
Mohammed Ahmed Alkailany, Mohammed Sadiq Abdalrazzaq
We formulate a new bond portfolio optimization model as a two-stage stochastic programming problem in which a decision maker can optimize the cost of bond portfolio selection while deciding which bonds to sell, which bonds to hold, and which bonds to buy from the market, as well as determine the quantity of additional cash in period t under different scenarios and varying assumptions, The model proved its efficiency by finding the optimal values and giving an investment plan that, it will reduce the cost of the portfolio.
{"title":"A new bond portfolio optimization model as two-stage stochastic programming problems in U.S. market","authors":"Mohammed Ahmed Alkailany, Mohammed Sadiq Abdalrazzaq","doi":"10.22075/IJNAA.2022.5771","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5771","url":null,"abstract":"We formulate a new bond portfolio optimization model as a two-stage stochastic programming problem in which a decision maker can optimize the cost of bond portfolio selection while deciding which bonds to sell, which bonds to hold, and which bonds to buy from the market, as well as determine the quantity of additional cash in period t under different scenarios and varying assumptions, The model proved its efficiency by finding the optimal values and giving an investment plan that, it will reduce the cost of the portfolio.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1545-1563"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68127882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2022.5785
A. Ningtyas, E. Nababan, S. Efendi
The K-Nearest Neighbor (KNN) method is often used by researchers for the classification process because it has a relatively great level of accuracy, however it also has a weakness which is sensitive of the noises. This research is aims to introduce an object recognition (identification) system of fingers leaves by classified using the KNN method. To resolves the weaknesses of the KNN method, the researcher has used the Local Binary Pattern (LBP) method to extract features of the leaves. For the comparison in feature extraction, the researcher has used the Gray Level Co-Occurrence Matrix (GLCM) method. The data that were used on this research are papaya leaves and chaya leaves (with the labels such as good and damage forms). In this research, an experimental design has been carried out that was differentiated by according to the comparison (of ratio) between training data and testing data (NI/Np), there were 90 training data and 45 testing data, where the feature extraction method used the 10 of features. Experimentally, it was shown that by using the ratio NI/Np = 67%:33%, the performance or system performance for classifying the images of fingers leaves by using the LBP extraction method showed that training data was obtained the results close to 95% and testing data was obtained the results close to 76%, while by using the GLCM extraction showed that training data was obtained the results close to 83% and testing data was obtained the results close to 58%.
{"title":"Performance analysis of local binary pattern and k-nearest neighbor on image classification of fingers leaves","authors":"A. Ningtyas, E. Nababan, S. Efendi","doi":"10.22075/IJNAA.2022.5785","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5785","url":null,"abstract":"The K-Nearest Neighbor (KNN) method is often used by researchers for the classification process because it has a relatively great level of accuracy, however it also has a weakness which is sensitive of the noises. This research is aims to introduce an object recognition (identification) system of fingers leaves by classified using the KNN method. To resolves the weaknesses of the KNN method, the researcher has used the Local Binary Pattern (LBP) method to extract features of the leaves. For the comparison in feature extraction, the researcher has used the Gray Level Co-Occurrence Matrix (GLCM) method. The data that were used on this research are papaya leaves and chaya leaves (with the labels such as good and damage forms). In this research, an experimental design has been carried out that was differentiated by according to the comparison (of ratio) between training data and testing data (NI/Np), there were 90 training data and 45 testing data, where the feature extraction method used the 10 of features. Experimentally, it was shown that by using the ratio NI/Np = 67%:33%, the performance or system performance for classifying the images of fingers leaves by using the LBP extraction method showed that training data was obtained the results close to 95% and testing data was obtained the results close to 76%, while by using the GLCM extraction showed that training data was obtained the results close to 83% and testing data was obtained the results close to 58%.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1701-1708"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68127929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/ijnaa.2022.6061
K. Alhasan, K. A. Al-Kadim
In this paper, we introduced the estimation of parameters for distributions that have multi-double truncation by the maximum likelihood method. We depended in the applied study on data of disease of Covid-19 by using one double truncation. Some statistical data were analyzed and unknown parameters and were compared with some distribution.
{"title":"Estimation of multi-truncated rayleigh and Weibull distributions with application","authors":"K. Alhasan, K. A. Al-Kadim","doi":"10.22075/ijnaa.2022.6061","DOIUrl":"https://doi.org/10.22075/ijnaa.2022.6061","url":null,"abstract":"In this paper, we introduced the estimation of parameters for distributions that have multi-double truncation by the maximum likelihood method. We depended in the applied study on data of disease of Covid-19 by using one double truncation. Some statistical data were analyzed and unknown parameters and were compared with some distribution.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68127964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2020.19923.2111
G. K. Gelian, R. Shirvani, M. A. Araghi
Here, the comparison between Sinc method in combination with double exponential transformations (DE) and approximation by means of differential transform method (DTM) for nonlinear Hammerstein integral equations is considered. Convergence analysis is presented. Detection of effectiveness from various aspects such as run time, different norms, condition number are highlighted and plotted graphically. Results of two schemes are practically well, but in manner of separable kernel, DTM solution is more accurate and so fast.
{"title":"Comparison between Sinc approximation and differential transform methods for nonlinear Hammerstein integral equations","authors":"G. K. Gelian, R. Shirvani, M. A. Araghi","doi":"10.22075/IJNAA.2020.19923.2111","DOIUrl":"https://doi.org/10.22075/IJNAA.2020.19923.2111","url":null,"abstract":"Here, the comparison between Sinc method in combination with double exponential transformations (DE) and approximation by means of differential transform method (DTM) for nonlinear Hammerstein integral equations is considered. Convergence analysis is presented. Detection of effectiveness from various aspects such as run time, different norms, condition number are highlighted and plotted graphically. Results of two schemes are practically well, but in manner of separable kernel, DTM solution is more accurate and so fast.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"25 1","pages":"1291-1301"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68115982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2020.21181.2240
Bagher Bagharzadehtvasani, A. Sheikhani, H. Aminikhah
In this paper we apply the Chebyshev polynomials method for the numerical solution of a class of variable-order fractional integro-differential equations with initial conditions. Moreover, a class of variable-order fractional integro-differential equations with fractional derivative of Caputo-Prabhakar sense is considered. The main aim of the Chebyshev polynomials method is to derive four kinds of operational matrices of Chebyshev polynomials. With such operational matrices, an equation is transformed into the products of several dependent matrices, which can also be viewed as the system of linear equations after dispersing the variables. Finally, numerical examples have been presented to demonstrate the accuracy of the proposed method, and the results have been compared with the exact solution.
{"title":"A numerical scheme for solving variable order Caputo-Prabhakar fractional integro-differential equation","authors":"Bagher Bagharzadehtvasani, A. Sheikhani, H. Aminikhah","doi":"10.22075/IJNAA.2020.21181.2240","DOIUrl":"https://doi.org/10.22075/IJNAA.2020.21181.2240","url":null,"abstract":"In this paper we apply the Chebyshev polynomials method for the numerical solution of a class of variable-order fractional integro-differential equations with initial conditions. Moreover, a class of variable-order fractional integro-differential equations with fractional derivative of Caputo-Prabhakar sense is considered. The main aim of the Chebyshev polynomials method is to derive four kinds of operational matrices of Chebyshev polynomials. With such operational matrices, an equation is transformed into the products of several dependent matrices, which can also be viewed as the system of linear equations after dispersing the variables. Finally, numerical examples have been presented to demonstrate the accuracy of the proposed method, and the results have been compared with the exact solution.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"38 1","pages":"467-484"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68116312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2021.23377.2525
Abdolkhalegh Vadian, M. Movahedi, A. Abri, M. Lotfi
Due to the nature of activities and processes, the petrochemical industry causes the production of industrial effluents, emissions and wastes that have adverse effects on the environment. The purpose of this study is to investigate the effect of petrochemical economic activities on environmental factors. In this paper, in order to minimize the costs and the amount of pollution caused by the emission of harmful gases, the closed-loop green supply chain model has been used, in which direct and reverse logistics networks have been considered. As a result, a fuzzy mathematical programming model has been developed for when the data are not definitively known. After the demand parameters and the amount of pollution are considered fuzzy, the maximum and bisector mean methods of the area are considered as methods (diffusion) of comparison and ranking of fuzzy definite numbers, and by adding Limitations of these two methods, the model was developed. To solve the model with real data, a plant from the petrochemical industry was selected and the data were prepared for a solution with very good estimates. Finally, the colonial competition algorithm was used to solve it. According to the model, its applicability was shown to reduce the number of environmental pollutants along with the reduction of transportation and waste, and the model for the closed-loop supply chain, which simultaneously considers two direct and inverse logistics networks. It is appropriate.
{"title":"The impact of petrochemical industry economic activities on environmental factors using a fuzzy mathematical programming model","authors":"Abdolkhalegh Vadian, M. Movahedi, A. Abri, M. Lotfi","doi":"10.22075/IJNAA.2021.23377.2525","DOIUrl":"https://doi.org/10.22075/IJNAA.2021.23377.2525","url":null,"abstract":"Due to the nature of activities and processes, the petrochemical industry causes the production of industrial effluents, emissions and wastes that have adverse effects on the environment. The purpose of this study is to investigate the effect of petrochemical economic activities on environmental factors. In this paper, in order to minimize the costs and the amount of pollution caused by the emission of harmful gases, the closed-loop green supply chain model has been used, in which direct and reverse logistics networks have been considered. As a result, a fuzzy mathematical programming model has been developed for when the data are not definitively known. After the demand parameters and the amount of pollution are considered fuzzy, the maximum and bisector mean methods of the area are considered as methods (diffusion) of comparison and ranking of fuzzy definite numbers, and by adding Limitations of these two methods, the model was developed. To solve the model with real data, a plant from the petrochemical industry was selected and the data were prepared for a solution with very good estimates. Finally, the colonial competition algorithm was used to solve it. According to the model, its applicability was shown to reduce the number of environmental pollutants along with the reduction of transportation and waste, and the model for the closed-loop supply chain, which simultaneously considers two direct and inverse logistics networks. It is appropriate.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"539-553"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68119396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2021.23520.2553
M. Ahmadi, Farzin Rezaei, N. Hamidi
Researchers have traditionally focused more on the quantity of company information disclosures, but in recent years, the quality of the information disclosed is more important than their quantity. On the other hand, the primary purpose of financial reporting is to provide useful information to stakeholders in relation to the conditions of the company to help investors' economic decisions, which is a function of the quality of the information provided by companies. Therefore, in the present study, by examining the opinions of experts and using the process of hierarchical analysis technique, the weight and importance of risk information disclosure criteria at three different levels (general, company specific and industry specific) were extracted in comparison, then by prioritizing them, Compatibility rate was calculated. Using statistical methods of two-way analysis of variance within the subject, it was concluded that there is no significant difference between the effect of risk information disclosure criteria on corporate investors' decision making.
{"title":"Evaluating the performance of company risk disclosure on improving the decision-making power of investors using hierarchical analysis technique(AHP)","authors":"M. Ahmadi, Farzin Rezaei, N. Hamidi","doi":"10.22075/IJNAA.2021.23520.2553","DOIUrl":"https://doi.org/10.22075/IJNAA.2021.23520.2553","url":null,"abstract":"Researchers have traditionally focused more on the quantity of company information disclosures, but in recent years, the quality of the information disclosed is more important than their quantity. On the other hand, the primary purpose of financial reporting is to provide useful information to stakeholders in relation to the conditions of the company to help investors' economic decisions, which is a function of the quality of the information provided by companies. Therefore, in the present study, by examining the opinions of experts and using the process of hierarchical analysis technique, the weight and importance of risk information disclosure criteria at three different levels (general, company specific and industry specific) were extracted in comparison, then by prioritizing them, Compatibility rate was calculated. Using statistical methods of two-way analysis of variance within the subject, it was concluded that there is no significant difference between the effect of risk information disclosure criteria on corporate investors' decision making.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"717-728"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68120256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2021.23619.2588
Allal Mehazzem, Mohamed Saleh Abdelouahab, K. Haouam
In this paper, we use the homoclinic orbit approach without using small perturbations to prove the existence of soliton solutions of the discrete nonlinear Schrodinger equations with long-range interaction by employing the properties of the symmetries of reversible planar maps. Moreover, the long-range interaction by a potential proportional to $1/l^{1+alpha} $ with fractional $alpha < 1 $ and $l $ as natural number.
{"title":"Homoclinic Orbits and Localized Solutions in Discrete Nonlinear Schrodinger Equation with Long-Range Interaction","authors":"Allal Mehazzem, Mohamed Saleh Abdelouahab, K. Haouam","doi":"10.22075/IJNAA.2021.23619.2588","DOIUrl":"https://doi.org/10.22075/IJNAA.2021.23619.2588","url":null,"abstract":"In this paper, we use the homoclinic orbit approach without using small perturbations to prove the existence of soliton solutions of the discrete nonlinear Schrodinger equations with long-range interaction by employing the properties of the symmetries of reversible planar maps. Moreover, the long-range interaction by a potential proportional to $1/l^{1+alpha} $ with fractional $alpha < 1 $ and $l $ as natural number.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"28 1","pages":"353-363"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68120265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2022.5788
M. Mechee, S. H. Aidi
A third-order fractional ordinary differential equation (FrODE) is very important in the mathematical modelling of physical problems. Generally, the third-order ODE is solved by converting the differential equation to a system of first-order ODEs. However, it is a lot more efficient in terms of accuracy, a number of function evaluations as well as computational time if the problem can be solved directly using numerical methods. In this paper, we are focused on the derivation of the direct numerical methods which are one, two and three-stage methods for solving third-order FrODEs. The RKD methods with two- and three stages for solving third-order ODEs are adapted for solving special third-order FrDEs. Numerical examples have been evaluated to show the effectiveness of the new methods compared with the analytical method. Numerical experiments are carried out to verify the accuracy and efficiency of the proposed methods. Applications of proposed methods are also presented which yield impressive results for the proposed and modified methods. The numerical solutions of the test problems using proposed methods agree well with the analytical solutions. From the numerical results obtained using proposed methods, we can conclude that the proposed methods in which derived or modified in this paper are very efficient.
{"title":"Generalized Euler and Runge-Kutta methods for solving classes of fractional ordinary differential equations","authors":"M. Mechee, S. H. Aidi","doi":"10.22075/IJNAA.2022.5788","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5788","url":null,"abstract":"A third-order fractional ordinary differential equation (FrODE) is very important in the mathematical modelling of physical problems. Generally, the third-order ODE is solved by converting the differential equation to a system of first-order ODEs. However, it is a lot more efficient in terms of accuracy, a number of function evaluations as well as computational time if the problem can be solved directly using numerical methods. In this paper, we are focused on the derivation of the direct numerical methods which are one, two and three-stage methods for solving third-order FrODEs. The RKD methods with two- and three stages for solving third-order ODEs are adapted for solving special third-order FrDEs. Numerical examples have been evaluated to show the effectiveness of the new methods compared with the analytical method. Numerical experiments are carried out to verify the accuracy and efficiency of the proposed methods. Applications of proposed methods are also presented which yield impressive results for the proposed and modified methods. The numerical solutions of the test problems using proposed methods agree well with the analytical solutions. From the numerical results obtained using proposed methods, we can conclude that the proposed methods in which derived or modified in this paper are very efficient.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1737-1745"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68127645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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