Abstract In the current paper, we introduce the notion of statistical convergence of order α and strongly p-Cesàro summability of order α of sequences in the gradual normed linear spaces. We investigate several properties and a few inclusion relations of the newly introduced notions.
{"title":"On statistical convergence of order α of sequences in gradual normed linear spaces","authors":"C. Choudhury, B. Das, S. Debnath","doi":"10.1515/jaa-2023-0105","DOIUrl":"https://doi.org/10.1515/jaa-2023-0105","url":null,"abstract":"Abstract In the current paper, we introduce the notion of statistical convergence of order α and strongly p-Cesàro summability of order α of sequences in the gradual normed linear spaces. We investigate several properties and a few inclusion relations of the newly introduced notions.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"13 12","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438646","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 We consider the l-th order linear fractional differential equations with constant coefficients. Here l ∈ ℕ {linmathbb{N}} is the ceiling for the highest derivative of order α, l - 1 < α ≤ l {l-1
Abstract We consider the l-th order linear fractional differential equations with constant coefficients.这里 l∈ ℕ {linmathbb{N}} 是最高导数 α 阶的上限，l - 1 < α ≤ l {l-1
{"title":"Existence and linear independence theorem for linear fractional differential equations with constant coefficients","authors":"P. Dubovski, J. Slepoi","doi":"10.1515/jaa-2023-0009","DOIUrl":"https://doi.org/10.1515/jaa-2023-0009","url":null,"abstract":"Abstract We consider the l-th order linear fractional differential equations with constant coefficients. Here l ∈ ℕ {linmathbb{N}} is the ceiling for the highest derivative of order α, l - 1 < α ≤ l {l-1<alphaleq l} . If β i < α {beta_{i}<alpha} are the other derivatives, the existing theory requires α - max { β i } ≥ l - 1 {alpha-max{beta_{i}}geq l-1} for the existence of l linearly independent solutions. Thus, at most one derivative may have order greater than one, but all other derivatives must be between zero and one. We remove this essential restriction and construct l linearly independent solutions. With this aim, we remodel the series approaches and elaborate the multi-sum fractional series method in order to obtain the existence and linear independence results. We consider both Riemann–Liouville or Caputo fractional derivatives.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"3 9","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438074","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 The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the Lie symmetry analysis of the time fractional Black–Scholes equation derived by the fractional Brownian motion. Some exact solutions are obtained, the figures of which are presented to illustrate the characteristics with different values of the parameters. In addition, a new conservation theorem and a generalization of the Noether operators are developed to construct the conservation laws for the time fractional Black–Scholes equation.
{"title":"Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion","authors":"Jicheng Yu","doi":"10.1515/jaa-2023-0107","DOIUrl":"https://doi.org/10.1515/jaa-2023-0107","url":null,"abstract":"Abstract The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the Lie symmetry analysis of the time fractional Black–Scholes equation derived by the fractional Brownian motion. Some exact solutions are obtained, the figures of which are presented to illustrate the characteristics with different values of the parameters. In addition, a new conservation theorem and a generalization of the Noether operators are developed to construct the conservation laws for the time fractional Black–Scholes equation.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"8 17","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438109","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}
Hrituraj Pal, Md Mirazul Hoque, B. Bhattacharya, J. Chakraborty
Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127–141]. This article begins with the introduction of 𝛿-ℐ-open covers in a mixed fuzzy ideal topological space. After that, we introduce 𝛿-ℐ-compactness and then some properties of its are discussed therein. It is shown that the aforesaid compactness is the weaker form of fuzzy compactness. Moreover, we show that if we retopologize the fuzzy topology then in the new environment fuzzy 𝛿-ℐ-compactness and fuzzy compactness are equivalent. In addition, we introduce two different notions of continuity and investigate the behavior between fuzzy 𝛿-ℐ-compactness and fuzzy compactness.
Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha].Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127-141].本文首先介绍混合模糊理想拓扑空间中的𝛿-ℐ-开盖。之后，我们介绍了𝛿-ℐ-紧密性，并讨论了其一些性质。研究表明，上述紧凑性是模糊紧凑性的弱形式。此外，我们还证明，如果我们重新拓扑模糊拓扑，那么在新的环境中，模糊𝛿-ℐ紧凑性和模糊紧凑性是等价的。此外，我们还引入了两种不同的连续性概念，并研究了模糊𝛿-ℐ紧凑性和模糊紧凑性之间的行为。
{"title":"A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space","authors":"Hrituraj Pal, Md Mirazul Hoque, B. Bhattacharya, J. Chakraborty","doi":"10.1515/jaa-2023-0163","DOIUrl":"https://doi.org/10.1515/jaa-2023-0163","url":null,"abstract":"Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127–141]. This article begins with the introduction of 𝛿-ℐ-open covers in a mixed fuzzy ideal topological space. After that, we introduce 𝛿-ℐ-compactness and then some properties of its are discussed therein. It is shown that the aforesaid compactness is the weaker form of fuzzy compactness. Moreover, we show that if we retopologize the fuzzy topology then in the new environment fuzzy 𝛿-ℐ-compactness and fuzzy compactness are equivalent. In addition, we introduce two different notions of continuity and investigate the behavior between fuzzy 𝛿-ℐ-compactness and fuzzy compactness.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"2 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438130","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":"139112774","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":"139112945","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":"139113728","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":"139114007","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":"139114194","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":"139114360","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：