Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.
{"title":"Side-side-angle triangle congruence axiom and the complete quadrilaterals","authors":"P. Csiba, L. Németh","doi":"10.3934/era.2023065","DOIUrl":"https://doi.org/10.3934/era.2023065","url":null,"abstract":"Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The degenerate versions of special polynomials and numbers, initiated by Carlitz, have regained the attention of some mathematicians by replacing the usual exponential function in the generating function of special polynomials with the degenerate exponential function. To study the relations between degenerate special polynomials, $ lambda $-umbral calculus, an analogue of umbral calculus, is intensively applied to obtain related formulas for expressing one $ lambda $-Sheffer polynomial in terms of other $ lambda $-Sheffer polynomials. In this paper, we study the connection between degenerate higher-order Daehee polynomials and other degenerate type of special polynomials. We present explicit formulas for representations of the polynomials using $ lambda $-umbral calculus and confirm the presented formulas between the degenerate higher-order Daehee polynomials and the degenerate Bernoulli polynomials, for example. Additionally, we investigate the pattern of the root distribution of these polynomials.
{"title":"Some identities of degenerate higher-order Daehee polynomials based on $ lambda $-umbral calculus","authors":"Dojin Kim, Sangbeom Park, J. Kwon","doi":"10.3934/era.2023155","DOIUrl":"https://doi.org/10.3934/era.2023155","url":null,"abstract":"The degenerate versions of special polynomials and numbers, initiated by Carlitz, have regained the attention of some mathematicians by replacing the usual exponential function in the generating function of special polynomials with the degenerate exponential function. To study the relations between degenerate special polynomials, $ lambda $-umbral calculus, an analogue of umbral calculus, is intensively applied to obtain related formulas for expressing one $ lambda $-Sheffer polynomial in terms of other $ lambda $-Sheffer polynomials. In this paper, we study the connection between degenerate higher-order Daehee polynomials and other degenerate type of special polynomials. We present explicit formulas for representations of the polynomials using $ lambda $-umbral calculus and confirm the presented formulas between the degenerate higher-order Daehee polynomials and the degenerate Bernoulli polynomials, for example. Additionally, we investigate the pattern of the root distribution of these polynomials.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Colorectal cancer (CRC) is one of the most popular cancers among both men and women, with increasing incidence. The enhanced analytical load data from the pathology laboratory, integrated with described intra- and inter-variabilities through the calculation of biomarkers, has prompted the quest for robust machine-based approaches in combination with routine practice. In histopathology, deep learning (DL) techniques have been applied at large due to their potential for supporting the analysis and forecasting of medically appropriate molecular phenotypes and microsatellite instability. Considering this background, the current research work presents a metaheuristics technique with deep convolutional neural network-based colorectal cancer classification based on histopathological imaging data (MDCNN-C3HI). The presented MDCNN-C3HI technique majorly examines the histopathological images for the classification of colorectal cancer (CRC). At the initial stage, the MDCNN-C3HI technique applies a bilateral filtering approach to get rid of the noise. Then, the proposed MDCNN-C3HI technique uses an enhanced capsule network with the Adam optimizer for the extraction of feature vectors. For CRC classification, the MDCNN-C3HI technique uses a DL modified neural network classifier, whereas the tunicate swarm algorithm is used to fine-tune its hyperparameters. To demonstrate the enhanced performance of the proposed MDCNN-C3HI technique on CRC classification, a wide range of experiments was conducted. The outcomes from the extensive experimentation procedure confirmed the superior performance of the proposed MDCNN-C3HI technique over other existing techniques, achieving a maximum accuracy of 99.45%, a sensitivity of 99.45% and a specificity of 99.45%.
{"title":"Tunicate swarm algorithm with deep convolutional neural network-driven colorectal cancer classification from histopathological imaging data","authors":"A. A. AL-Ghamdi, Mahmoud Ragab","doi":"10.3934/era.2023141","DOIUrl":"https://doi.org/10.3934/era.2023141","url":null,"abstract":"Colorectal cancer (CRC) is one of the most popular cancers among both men and women, with increasing incidence. The enhanced analytical load data from the pathology laboratory, integrated with described intra- and inter-variabilities through the calculation of biomarkers, has prompted the quest for robust machine-based approaches in combination with routine practice. In histopathology, deep learning (DL) techniques have been applied at large due to their potential for supporting the analysis and forecasting of medically appropriate molecular phenotypes and microsatellite instability. Considering this background, the current research work presents a metaheuristics technique with deep convolutional neural network-based colorectal cancer classification based on histopathological imaging data (MDCNN-C3HI). The presented MDCNN-C3HI technique majorly examines the histopathological images for the classification of colorectal cancer (CRC). At the initial stage, the MDCNN-C3HI technique applies a bilateral filtering approach to get rid of the noise. Then, the proposed MDCNN-C3HI technique uses an enhanced capsule network with the Adam optimizer for the extraction of feature vectors. For CRC classification, the MDCNN-C3HI technique uses a DL modified neural network classifier, whereas the tunicate swarm algorithm is used to fine-tune its hyperparameters. To demonstrate the enhanced performance of the proposed MDCNN-C3HI technique on CRC classification, a wide range of experiments was conducted. The outcomes from the extensive experimentation procedure confirmed the superior performance of the proposed MDCNN-C3HI technique over other existing techniques, achieving a maximum accuracy of 99.45%, a sensitivity of 99.45% and a specificity of 99.45%.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a topology optimization algorithm for the mechanical-electrical coupling problem of periodic composite materials is studied. Firstly, the homogenization problem of the mechanical-electrical coupling topology optimization problem of periodic composite materials is established by the multi-scale asymptotic expansion method. Secondly, the topology optimization algorithm for the mechanical-electrical coupling problem of periodic composite materials is constructed by finite element method, solid isotropic material with penalisation method and homogenization method. Finally, numerical results show that the proposed algorithm is effective to calculate the optimal structure of the periodic composite cantilever beam under the influence of the mechanical-electrical coupling.
{"title":"Topological optimization algorithm for mechanical-electrical coupling of periodic composite materials","authors":"Ziqiang Wang, Chunyu Cen, Junying Cao","doi":"10.3934/era.2023136","DOIUrl":"https://doi.org/10.3934/era.2023136","url":null,"abstract":"In this paper, a topology optimization algorithm for the mechanical-electrical coupling problem of periodic composite materials is studied. Firstly, the homogenization problem of the mechanical-electrical coupling topology optimization problem of periodic composite materials is established by the multi-scale asymptotic expansion method. Secondly, the topology optimization algorithm for the mechanical-electrical coupling problem of periodic composite materials is constructed by finite element method, solid isotropic material with penalisation method and homogenization method. Finally, numerical results show that the proposed algorithm is effective to calculate the optimal structure of the periodic composite cantilever beam under the influence of the mechanical-electrical coupling.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Manal Abdullah Alohali, M. Maashi, Raji Faqih, Hany Mahgoub, Abdullah Mohamed, Mohammed Assiri, Suhanda Drar
Traffic surveillance systems are utilized to collect and monitor the traffic condition data of the road networks. This data plays a crucial role in a variety of applications of the Intelligent Transportation Systems (ITSs). In traffic surveillance, it is challenging to achieve accurate vehicle detection and count the vehicles from traffic videos. The most notable difficulties include real-time system operations for precise classification, identification of the vehicles' location in traffic flows and functioning around total occlusions that hamper the vehicle tracking process. Conventional video-related vehicle detection techniques such as optical flow, background subtraction and frame difference have certain limitations in terms of efficiency or accuracy. Therefore, the current study proposes to design the spotted hyena optimizer with deep learning-enabled vehicle counting and classification (SHODL-VCC) model for the ITSs. The aim of the proposed SHODL-VCC technique lies in accurate counting and classification of the vehicles in traffic surveillance. To achieve this, the proposed SHODL-VCC technique follows a two-stage process that includes vehicle detection and vehicle classification. Primarily, the presented SHODL-VCC technique employs the RetinaNet object detector to identify the vehicles. Next, the detected vehicles are classified into different class labels using the deep wavelet auto-encoder model. To enhance the vehicle detection performance, the spotted hyena optimizer algorithm is exploited as a hyperparameter optimizer, which considerably enhances the vehicle detection rate. The proposed SHODL-VCC technique was experimentally validated using different databases. The comparative outcomes demonstrate the promising vehicle classification performance of the SHODL-VCC technique in comparison with recent deep learning approaches.
{"title":"Spotted hyena optimizer with deep learning enabled vehicle counting and classification model for intelligent transportation systems","authors":"Manal Abdullah Alohali, M. Maashi, Raji Faqih, Hany Mahgoub, Abdullah Mohamed, Mohammed Assiri, Suhanda Drar","doi":"10.3934/era.2023188","DOIUrl":"https://doi.org/10.3934/era.2023188","url":null,"abstract":"Traffic surveillance systems are utilized to collect and monitor the traffic condition data of the road networks. This data plays a crucial role in a variety of applications of the Intelligent Transportation Systems (ITSs). In traffic surveillance, it is challenging to achieve accurate vehicle detection and count the vehicles from traffic videos. The most notable difficulties include real-time system operations for precise classification, identification of the vehicles' location in traffic flows and functioning around total occlusions that hamper the vehicle tracking process. Conventional video-related vehicle detection techniques such as optical flow, background subtraction and frame difference have certain limitations in terms of efficiency or accuracy. Therefore, the current study proposes to design the spotted hyena optimizer with deep learning-enabled vehicle counting and classification (SHODL-VCC) model for the ITSs. The aim of the proposed SHODL-VCC technique lies in accurate counting and classification of the vehicles in traffic surveillance. To achieve this, the proposed SHODL-VCC technique follows a two-stage process that includes vehicle detection and vehicle classification. Primarily, the presented SHODL-VCC technique employs the RetinaNet object detector to identify the vehicles. Next, the detected vehicles are classified into different class labels using the deep wavelet auto-encoder model. To enhance the vehicle detection performance, the spotted hyena optimizer algorithm is exploited as a hyperparameter optimizer, which considerably enhances the vehicle detection rate. The proposed SHODL-VCC technique was experimentally validated using different databases. The comparative outcomes demonstrate the promising vehicle classification performance of the SHODL-VCC technique in comparison with recent deep learning approaches.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raúl M. Falcón, V. Álvarez, J. Armario, M. Frau, F. Gudiel, M. Güemes
Based on the binary product described by any Latin square, the Hadamard quasigroup product is introduced in this paper as a natural generalization of the classical Hadamard product of matrices. The successive iteration of this new product is endowed with a cyclic behaviour that enables one to define a pair of new isomorphism invariants of Latin squares. Of particular interest is the set of Latin squares for which this iteration preserves the Latin square property, which requires the existence of successive localized Latin transversals within the Latin square under consideration. In order to enumerate and classify, up to isomorphism, these Latin squares, we propose a computational algebraic geometry approach based on the computation of reduced Gröbner bases. To illustrate this point, we obtain the classification of the sought Latin squares, for order up to six, by using the open computer algebra system for polynomial computations Singular.
{"title":"A computational approach to analyze the Hadamard quasigroup product","authors":"Raúl M. Falcón, V. Álvarez, J. Armario, M. Frau, F. Gudiel, M. Güemes","doi":"10.3934/era.2023164","DOIUrl":"https://doi.org/10.3934/era.2023164","url":null,"abstract":"Based on the binary product described by any Latin square, the Hadamard quasigroup product is introduced in this paper as a natural generalization of the classical Hadamard product of matrices. The successive iteration of this new product is endowed with a cyclic behaviour that enables one to define a pair of new isomorphism invariants of Latin squares. Of particular interest is the set of Latin squares for which this iteration preserves the Latin square property, which requires the existence of successive localized Latin transversals within the Latin square under consideration. In order to enumerate and classify, up to isomorphism, these Latin squares, we propose a computational algebraic geometry approach based on the computation of reduced Gröbner bases. To illustrate this point, we obtain the classification of the sought Latin squares, for order up to six, by using the open computer algebra system for polynomial computations Singular.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lijing Ma, Shiru Qu, Lijun Song, Junxi Zhang, J. Ren
Incorporating human driving style into car-following modeling is critical for achieving higher levels of driving automation. By capturing the characteristics of human driving, it can lead to a more natural and seamless transition from human-driven to automated driving. A clustering approach is introduced that utilized principal component analysis (PCA) and k-means clustering algorithm to identify driving style types such as aggressive, moderate and conservative at the timestep level. Additionally, an online driving style recognition technique is developed based on the memory effect in driving behavior, allowing for real-time identification of a driver's driving style and enabling adaptive control in automated driving. Finally, the Intelligent Driver Model (IDM) has been improved through the incorporation of an online driving style recognition strategy into car-following modeling, resulting in a human-like IDM that emulates real-world driving behaviors. This enhancement has important implications for the field of automated driving, as it allows for greater accuracy and adaptability in modeling human driving behavior and may ultimately lead to more effective and seamless transitions between human-driven and automated driving modes. The results show that the time-step level driving style recognition method provides a more precise understanding of driving styles that accounts for both inter-driver heterogeneity and intra-driver variation. The proposed human-like IDM performs well in capturing driving style characteristics and reproducing driving behavior. The stability of this improved human-like IDM is also confirmed, indicating its reliability and effectiveness. Overall, the research suggests that the proposed model has promising performance and potential applications in the field of automated driving.
{"title":"Human-like car-following modeling based on online driving style recognition","authors":"Lijing Ma, Shiru Qu, Lijun Song, Junxi Zhang, J. Ren","doi":"10.3934/era.2023165","DOIUrl":"https://doi.org/10.3934/era.2023165","url":null,"abstract":"Incorporating human driving style into car-following modeling is critical for achieving higher levels of driving automation. By capturing the characteristics of human driving, it can lead to a more natural and seamless transition from human-driven to automated driving. A clustering approach is introduced that utilized principal component analysis (PCA) and k-means clustering algorithm to identify driving style types such as aggressive, moderate and conservative at the timestep level. Additionally, an online driving style recognition technique is developed based on the memory effect in driving behavior, allowing for real-time identification of a driver's driving style and enabling adaptive control in automated driving. Finally, the Intelligent Driver Model (IDM) has been improved through the incorporation of an online driving style recognition strategy into car-following modeling, resulting in a human-like IDM that emulates real-world driving behaviors. This enhancement has important implications for the field of automated driving, as it allows for greater accuracy and adaptability in modeling human driving behavior and may ultimately lead to more effective and seamless transitions between human-driven and automated driving modes. The results show that the time-step level driving style recognition method provides a more precise understanding of driving styles that accounts for both inter-driver heterogeneity and intra-driver variation. The proposed human-like IDM performs well in capturing driving style characteristics and reproducing driving behavior. The stability of this improved human-like IDM is also confirmed, indicating its reliability and effectiveness. Overall, the research suggests that the proposed model has promising performance and potential applications in the field of automated driving.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current paper is devoted to the stochastic $ N $-species cooperative system with a moderately strong noise. By the theory of monotone random systems and the technique of suitable marker of wavefront, the existence of the travelling wave solution is established. By applying the Feynman-Kac formula and sup-sub solution technique, the upper and lower bounded of the asymptotic wave speed are also obtained. Finally, we give an example for stochastic 3-species cooperative systems.
{"title":"Stochastic travelling wave solution of the $ N $-species cooperative systems with multiplicative noise","authors":"Hao Wen, Yantao Luo, Jianhua Huang, Yuhong Li","doi":"10.3934/era.2023225","DOIUrl":"https://doi.org/10.3934/era.2023225","url":null,"abstract":"The current paper is devoted to the stochastic $ N $-species cooperative system with a moderately strong noise. By the theory of monotone random systems and the technique of suitable marker of wavefront, the existence of the travelling wave solution is established. By applying the Feynman-Kac formula and sup-sub solution technique, the upper and lower bounded of the asymptotic wave speed are also obtained. Finally, we give an example for stochastic 3-species cooperative systems.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to European Union (EU) oil sanctions, tanker shipping companies need to redeploy their tankers by moving tankers between ship routes with the consideration of flag states of tankers, but the literature lacks quantitative methods for this problem. To fill this research gap, this paper studies an integrated problem of fleet deployment, fleet repositioning, round trip completion, and speed optimization with the consideration of flag states of tankers. The problem is formulated as a nonlinear integer programming model to minimize the total cost, including the fleet repositioning cost, the mismatch cost, and the fuel cost, during the planning period while satisfying the total crude oil transportation demand of each voyage and the minimum shipping frequency. Some linearization methods are used to transform the nonlinear model to a linear one which can be directly solved by Gurobi. The average solving time required for 17 computational instances is 4.5 minutes, which validates the effectiveness of the proposed model. Sensitivity analyses, including the influences of the unit fuel price, the total crude oil transportation demand, the mismatch cost of completing a round trip by a deployed tanker, and the repositioning cost for each deployed tanker, on operations decisions, are conducted to obtain managerial insights.
{"title":"New challenges in fleet deployment considering EU oil sanctions","authors":"Yiwei Wu, Yao Lu, Shuaian Wang, Lu Zhen","doi":"10.3934/era.2023230","DOIUrl":"https://doi.org/10.3934/era.2023230","url":null,"abstract":"Due to European Union (EU) oil sanctions, tanker shipping companies need to redeploy their tankers by moving tankers between ship routes with the consideration of flag states of tankers, but the literature lacks quantitative methods for this problem. To fill this research gap, this paper studies an integrated problem of fleet deployment, fleet repositioning, round trip completion, and speed optimization with the consideration of flag states of tankers. The problem is formulated as a nonlinear integer programming model to minimize the total cost, including the fleet repositioning cost, the mismatch cost, and the fuel cost, during the planning period while satisfying the total crude oil transportation demand of each voyage and the minimum shipping frequency. Some linearization methods are used to transform the nonlinear model to a linear one which can be directly solved by Gurobi. The average solving time required for 17 computational instances is 4.5 minutes, which validates the effectiveness of the proposed model. Sensitivity analyses, including the influences of the unit fuel price, the total crude oil transportation demand, the mismatch cost of completing a round trip by a deployed tanker, and the repositioning cost for each deployed tanker, on operations decisions, are conducted to obtain managerial insights.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop a numerical method by using operational matrices based on Hosoya polynomials of simple paths to find the approximate solution of diffusion equations of fractional order with respect to time. This method is applied to certain diffusion equations like time fractional advection-diffusion equations and time fractional Kolmogorov equations. Here we use the Atangana-Baleanu fractional derivative. With the help of this approach we convert these equations to a set of algebraic equations, which is easier to be solved. Also, the error bound is provided. The obtained numerical solutions using the presented method are compared with the exact solutions. The numerical results show that the suggested method is convenient and accurate.
{"title":"Numerical study for a class of time fractional diffusion equations using operational matrices based on Hosoya polynomial","authors":"Ping Zhou, H. Jafari, R. Ganji, S. Narsale","doi":"10.3934/era.2023231","DOIUrl":"https://doi.org/10.3934/era.2023231","url":null,"abstract":"In this paper, we develop a numerical method by using operational matrices based on Hosoya polynomials of simple paths to find the approximate solution of diffusion equations of fractional order with respect to time. This method is applied to certain diffusion equations like time fractional advection-diffusion equations and time fractional Kolmogorov equations. Here we use the Atangana-Baleanu fractional derivative. With the help of this approach we convert these equations to a set of algebraic equations, which is easier to be solved. Also, the error bound is provided. The obtained numerical solutions using the presented method are compared with the exact solutions. The numerical results show that the suggested method is convenient and accurate.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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