Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
{"title":"Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations","authors":"Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk","doi":"10.1515/jaa-2023-0029","DOIUrl":"https://doi.org/10.1515/jaa-2023-0029","url":null,"abstract":"Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123169","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}
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
{"title":"Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations","authors":"Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk","doi":"10.1515/jaa-2023-0029","DOIUrl":"https://doi.org/10.1515/jaa-2023-0029","url":null,"abstract":"Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123435","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}
Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.
Abstract 本文通过高阶连续性模量证明了拉盖尔超群 K = [ 0 , + ∞ [ × R 的 Titchmarsh 定理（Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R}, via moduli of continuity of higher orders.
{"title":"Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup","authors":"L. Rakhimi, Radouan Daher","doi":"10.1515/jaa-2023-0035","DOIUrl":"https://doi.org/10.1515/jaa-2023-0035","url":null,"abstract":"Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"44 12","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123948","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}
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
{"title":"Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations","authors":"Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk","doi":"10.1515/jaa-2023-0029","DOIUrl":"https://doi.org/10.1515/jaa-2023-0029","url":null,"abstract":"Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139112642","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}
Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.
Abstract 本文通过高阶连续性模量证明了拉盖尔超群 K = [ 0 , + ∞ [ × R 的 Titchmarsh 定理（Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R}, via moduli of continuity of higher orders.
{"title":"Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup","authors":"L. Rakhimi, Radouan Daher","doi":"10.1515/jaa-2023-0035","DOIUrl":"https://doi.org/10.1515/jaa-2023-0035","url":null,"abstract":"Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"44 12","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139114250","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}
Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.
Abstract 本文通过高阶连续性模量证明了拉盖尔超群 K = [ 0 , + ∞ [ × R 的 Titchmarsh 定理（Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R}, via moduli of continuity of higher orders.
{"title":"Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup","authors":"L. Rakhimi, Radouan Daher","doi":"10.1515/jaa-2023-0035","DOIUrl":"https://doi.org/10.1515/jaa-2023-0035","url":null,"abstract":"Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"44 12","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139116778","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}
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
{"title":"Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations","authors":"Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk","doi":"10.1515/jaa-2023-0029","DOIUrl":"https://doi.org/10.1515/jaa-2023-0029","url":null,"abstract":"Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139117208","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}
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
{"title":"Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations","authors":"Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk","doi":"10.1515/jaa-2023-0029","DOIUrl":"https://doi.org/10.1515/jaa-2023-0029","url":null,"abstract":"Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139118027","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}
Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.
Abstract 本文通过高阶连续性模量证明了拉盖尔超群 K = [ 0 , + ∞ [ × R 的 Titchmarsh 定理（Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R}, via moduli of continuity of higher orders.
{"title":"Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup","authors":"L. Rakhimi, Radouan Daher","doi":"10.1515/jaa-2023-0035","DOIUrl":"https://doi.org/10.1515/jaa-2023-0035","url":null,"abstract":"Abstract In this paper, we prove the Titchmarsh theorem for Laguerre hypergroup K = [ 0 , + ∞ [ × R mathbb{K}=[0,+inftymathclose{[}timesmathbb{R} , via moduli of continuity of higher orders.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"44 12","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139118038","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}
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
{"title":"Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations","authors":"Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk","doi":"10.1515/jaa-2023-0029","DOIUrl":"https://doi.org/10.1515/jaa-2023-0029","url":null,"abstract":"Abstract This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139118734","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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