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On statistical convergence of order α of sequences in gradual normed linear spaces 论渐变规范线性空间中序列秩 α 的统计收敛性
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-11 DOI: 10.1515/jaa-2023-0105
C. Choudhury, B. Das, S. Debnath
{"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}
引用次数: 0
Existence and linear independence theorem for linear fractional differential equations with constant coefficients 具有常数系数的线性分数微分方程的存在性和线性独立性定理
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-11 DOI: 10.1515/jaa-2023-0009
P. Dubovski, J. Slepoi
{"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}
引用次数: 0
Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion 由分数布朗运动导出的时间分数布莱克-斯科尔斯方程的列对称性、精确解和守恒定律
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-11 DOI: 10.1515/jaa-2023-0107
Jicheng Yu
{"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}
引用次数: 0
A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space 混合模糊理想拓扑空间中的δ-ℐ紧密性研究
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-11 DOI: 10.1515/jaa-2023-0163
Hrituraj Pal, Md Mirazul Hoque, B. Bhattacharya, J. Chakraborty
{"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}
引用次数: 0
Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations 应用 Touchard 小波模拟分数受电弓微分方程的数值解
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-03 DOI: 10.1515/jaa-2023-0029
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
{"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}
引用次数: 0
Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations 应用 Touchard 小波模拟分数受电弓微分方程的数值解
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-03 DOI: 10.1515/jaa-2023-0029
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
{"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}
引用次数: 0
Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup 具有拉盖尔超群连续性模量的蒂奇马什定理
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-03 DOI: 10.1515/jaa-2023-0035
L. Rakhimi, Radouan Daher
{"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}
引用次数: 0
Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations 应用 Touchard 小波模拟分数受电弓微分方程的数值解
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-03 DOI: 10.1515/jaa-2023-0029
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
{"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}
引用次数: 0
Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup 具有拉盖尔超群连续性模量的蒂奇马什定理
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-03 DOI: 10.1515/jaa-2023-0035
L. Rakhimi, Radouan Daher
{"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}
引用次数: 0
Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations 应用 Touchard 小波模拟分数受电弓微分方程的数值解
IF 0.9
Journal of Applied Analysis Pub Date : 2024-01-03 DOI: 10.1515/jaa-2023-0029
Mostafa Safavi, A. Khajehnasiri, Reza Ezzati, Saeedeh Rezabeyk
{"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}
引用次数: 0
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