Pub Date : 2023-10-30DOI: 10.28924/2291-8639-21-2023-120
B. Divya, K. Ganesan
Modelling several real-world issues in the fuzzy world extensively uses ordinary differential equations. In this paper, a mechanical vibration system with the given mass, spring constant, damping and external force is modelled as a second-order ordinary differential equation. Due to measurement errors, the initial displacement of the string is approximate and assumed to be a fuzzy number. A fuzzy version of the Sumudu transform procedure is used to figure out this vibrating spring-mass system with fuzzy initial displacement. The output is displayed as a table at various computational stages. The consequences are visibly presented diagrammatically for different values of r and t. There is a good agreement between the computed results and the analytical solution.
{"title":"Applications of Fuzzy Differential Equations on Vibrating Spring Mass System","authors":"B. Divya, K. Ganesan","doi":"10.28924/2291-8639-21-2023-120","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-120","url":null,"abstract":"Modelling several real-world issues in the fuzzy world extensively uses ordinary differential equations. In this paper, a mechanical vibration system with the given mass, spring constant, damping and external force is modelled as a second-order ordinary differential equation. Due to measurement errors, the initial displacement of the string is approximate and assumed to be a fuzzy number. A fuzzy version of the Sumudu transform procedure is used to figure out this vibrating spring-mass system with fuzzy initial displacement. The output is displayed as a table at various computational stages. The consequences are visibly presented diagrammatically for different values of r and t. There is a good agreement between the computed results and the analytical solution.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"73 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136067787","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 : 2023-10-30DOI: 10.28924/2291-8639-21-2023-118
Prapart Pue-on
The Double Sadik Transform (DST) represents a generalized double integral transform that has emerged as a highly effective analytical technique for solving numerous scientific problems. This study aims to investigate the DST applied to elementary functions and explore its notable properties, including its duality with the Double Laplace Transform and its capability to transform shifting functions, periodic functions, and convolution functions. Furthermore, the DST methodology is employed to resolve prominent linear fractional Caputo partial differential equations with known solutions commonly encountered in diverse mathematical models. The obtained outcomes are expressed in exact closed form, with the most precise results articulated through the Mittag-Leffler function. These results serve to validate the effectiveness and efficiency of the DST approach, establishing it as a valuable tool for addressing scientific problems involving fractional calculus.
{"title":"Exploring the Remarkable Properties of the Double Sadik Transform and Its Applications to Fractional Caputo Partial Differential Equations","authors":"Prapart Pue-on","doi":"10.28924/2291-8639-21-2023-118","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-118","url":null,"abstract":"The Double Sadik Transform (DST) represents a generalized double integral transform that has emerged as a highly effective analytical technique for solving numerous scientific problems. This study aims to investigate the DST applied to elementary functions and explore its notable properties, including its duality with the Double Laplace Transform and its capability to transform shifting functions, periodic functions, and convolution functions. Furthermore, the DST methodology is employed to resolve prominent linear fractional Caputo partial differential equations with known solutions commonly encountered in diverse mathematical models. The obtained outcomes are expressed in exact closed form, with the most precise results articulated through the Mittag-Leffler function. These results serve to validate the effectiveness and efficiency of the DST approach, establishing it as a valuable tool for addressing scientific problems involving fractional calculus.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103479","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 : 2023-10-23DOI: 10.28924/2291-8639-21-2023-116
Junaid Ahmad, Muhammad Arshad, Hasanen A. Hammad, Doha A. Kattan
In this manuscript, we suggest a three-step iterative scheme for finding approximate numerical solutions to boundary value problems (BVPs) in a Banach space setting. The underlying strategy of the scheme is based on embedding Green’s function into the three-step M-iterative scheme, which we will call in the paper M-Green’s iterative scheme. We assume certain possible mild conditions to prove the convergence and stability results of the suggested scheme. We also prove numerically that our M-Green iterative scheme is more effective than the corresponding Mann-Green and Khan-Green iterative schemes. Our results improve and extend some recent results in the literature of Green’s function based iteration schemes.
{"title":"A Three-Step Iterative Scheme Based on Green's Function for the Solution of Boundary Value Problems","authors":"Junaid Ahmad, Muhammad Arshad, Hasanen A. Hammad, Doha A. Kattan","doi":"10.28924/2291-8639-21-2023-116","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-116","url":null,"abstract":"In this manuscript, we suggest a three-step iterative scheme for finding approximate numerical solutions to boundary value problems (BVPs) in a Banach space setting. The underlying strategy of the scheme is based on embedding Green’s function into the three-step M-iterative scheme, which we will call in the paper M-Green’s iterative scheme. We assume certain possible mild conditions to prove the convergence and stability results of the suggested scheme. We also prove numerically that our M-Green iterative scheme is more effective than the corresponding Mann-Green and Khan-Green iterative schemes. Our results improve and extend some recent results in the literature of Green’s function based iteration schemes.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135412961","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 : 2023-10-23DOI: 10.28924/2291-8639-21-2023-117
Abderrahman Baza, Mohamed Rossafi
In this work, we investigate the generalised Hyers-Ulam stability of additive functional inequality in modular spaces with ∆2-conditions and in β-homogeneous Banach spaces.
{"title":"Generalized Hyers-Ulam Stability of Additive Functional Inequality in Modular Spaces and β-Homogeneous Banach Spaces","authors":"Abderrahman Baza, Mohamed Rossafi","doi":"10.28924/2291-8639-21-2023-117","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-117","url":null,"abstract":"In this work, we investigate the generalised Hyers-Ulam stability of additive functional inequality in modular spaces with ∆2-conditions and in β-homogeneous Banach spaces.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135413540","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 : 2023-10-23DOI: 10.28924/2291-8639-21-2023-115
Aiyared Iampan, N. Rajesh
In this paper, the concepts of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras and (∈, ∈)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are introduced and studied. The UP (BCC)-homomorphic image and inverse image are investigated in (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras. Characterizations of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are discussed.
本文引入并研究了(∈，∈∨q)-反直觉模糊软UP (BCC)-子代数和(∈，∈)-反直觉模糊软UP (BCC)- UP (BCC)-代数的子代数概念。在(∈，∈∨q)-反直觉模糊软UP (BCC)- UP (BCC)-代数的子代数中研究UP (BCC)-同态象和逆象。讨论了(∈，∈∨q)-反直觉模糊软UP (BCC)- UP (BCC)-代数的子代数。
{"title":"Characterizing (∈, ∈∨q)-Anti-Intuitionistic Fuzzy Soft UP (BCC)-Subalgebras of UP (BCC)-Algebras","authors":"Aiyared Iampan, N. Rajesh","doi":"10.28924/2291-8639-21-2023-115","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-115","url":null,"abstract":"In this paper, the concepts of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras and (∈, ∈)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are introduced and studied. The UP (BCC)-homomorphic image and inverse image are investigated in (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras. Characterizations of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are discussed.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"48 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135366469","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 : 2023-10-12DOI: 10.28924/2291-8639-21-2023-114
E. Muthu Meena Lakshmanan, K. Suja
In the present research paper, an investigation is undertaken of Steinhaus type theorems for Nörlund-(M, λn) and Nörlund-Euler(M, λn) method of summability in K, a complete non-trivially valued Non-Archimedean field. The conditions for statistical summability for those matrices are discussed in such fields K. The consistency of Nörlund-(M, λn) method of summability is investigated when different sequences are used in the summation process. Further, the relation between Nörlund-Euler(M, λn) summable and its statistical summability is also established.
{"title":"Steinhaus Type Theorem for Nörlund-(M, λn) and Nörlund-Euler-(M, λn) Methods of Summability in Non-Archimedean Fields","authors":"E. Muthu Meena Lakshmanan, K. Suja","doi":"10.28924/2291-8639-21-2023-114","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-114","url":null,"abstract":"In the present research paper, an investigation is undertaken of Steinhaus type theorems for Nörlund-(M, λn) and Nörlund-Euler(M, λn) method of summability in K, a complete non-trivially valued Non-Archimedean field. The conditions for statistical summability for those matrices are discussed in such fields K. The consistency of Nörlund-(M, λn) method of summability is investigated when different sequences are used in the summation process. Further, the relation between Nörlund-Euler(M, λn) summable and its statistical summability is also established.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"248 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136013449","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 : 2023-10-12DOI: 10.28924/2291-8639-21-2023-113
Iqbal H. Jebril, Mohammed S. El-Khatib, Ahmad A. Abubaker, Suha B. Al-Shaikh, Iqbal M. Batiha
In this paper, we introduce and develop a new definitions for Katugampola derivative and Katugampola integral. In particular, we defined a (left) fractional derivative starting from a of a function f of order α∈(m-1, m] and a (right) fractional derivative terminating at b, where m ∈ N. Then, we give some proprieties in relation to these operators such as linearity, product rule, quotient rule, power rule, chain rule, and vanishing derivatives for constant functions.
{"title":"Results on Katugampola Fractional Derivatives and Integrals","authors":"Iqbal H. Jebril, Mohammed S. El-Khatib, Ahmad A. Abubaker, Suha B. Al-Shaikh, Iqbal M. Batiha","doi":"10.28924/2291-8639-21-2023-113","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-113","url":null,"abstract":"In this paper, we introduce and develop a new definitions for Katugampola derivative and Katugampola integral. In particular, we defined a (left) fractional derivative starting from a of a function f of order α∈(m-1, m] and a (right) fractional derivative terminating at b, where m ∈ N. Then, we give some proprieties in relation to these operators such as linearity, product rule, quotient rule, power rule, chain rule, and vanishing derivatives for constant functions.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135967755","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 : 2023-10-04DOI: 10.28924/2291-8639-21-2023-108
Eltiyeb Ali
In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this property relates to the p.q.-Baer property of R and the existence of a generalized join in I(R) for M-indexed subsets, where I(R) denotes the set of ideals of R. Additionally, we prove a connection between R being a left p.q.-Baer ring and the CM-quasi-Armendariz property. Moreover, we prove that for any element φ2=φ, there exist an idempotent element e2=e such that φ = ce. We then prove that R is quasi-Baer if and only if the crossed product structure R⋊M is quasi-Baer. Finally, we present novel results regarding various constructions for crossed products.
{"title":"On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings","authors":"Eltiyeb Ali","doi":"10.28924/2291-8639-21-2023-108","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-108","url":null,"abstract":"In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this property relates to the p.q.-Baer property of R and the existence of a generalized join in I(R) for M-indexed subsets, where I(R) denotes the set of ideals of R. Additionally, we prove a connection between R being a left p.q.-Baer ring and the CM-quasi-Armendariz property. Moreover, we prove that for any element φ2=φ, there exist an idempotent element e2=e such that φ = ce. We then prove that R is quasi-Baer if and only if the crossed product structure R⋊M is quasi-Baer. Finally, we present novel results regarding various constructions for crossed products.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590487","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 : 2023-10-04DOI: 10.28924/2291-8639-21-2023-109
Belabbaci Chafika
In this paper, we give several characterizations of the Jeribi essential spectrum of a bounded linear operator defined on a Banach space by using the notion of almost weakly compact operators. As a consequence, we prove the stability of the Jeribi essential spectrum under compact perturbations. Furthermore, some characterizations of the Jeribi essential spectra of 3×3 upper triangular block operator matrix are also given.
{"title":"New Characterizations of the Jeribi Essential Spectrum","authors":"Belabbaci Chafika","doi":"10.28924/2291-8639-21-2023-109","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-109","url":null,"abstract":"In this paper, we give several characterizations of the Jeribi essential spectrum of a bounded linear operator defined on a Banach space by using the notion of almost weakly compact operators. As a consequence, we prove the stability of the Jeribi essential spectrum under compact perturbations. Furthermore, some characterizations of the Jeribi essential spectra of 3×3 upper triangular block operator matrix are also given.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"187 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135593797","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 : 2023-10-04DOI: 10.28924/2291-8639-21-2023-112
Doha A. Kattan, Hasanen A. Hammad
The psychological learning theory (PLT) in the formation of moral verdict is represented by the choice-practice paradigm. It involves weighing the effects of various options and choosing one to put into practice. This manuscript is devoted to presenting a general functional equation (FE) for observing animal behavior in such situations. The proposed equation can be used to explain a number of well-known learning and psychological theories. The existence and uniqueness of the solution to a given equation are demonstrated using fixed point (FP) techniques. Furthermore, the stability of the solution to the provided FE is explored in the sense of Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU). Ultimately, to emphasize the importance of our results, two examples are presented.
{"title":"A Solution of a General Functional Equation Involved in Psychological Theory of Learning and Stability Results","authors":"Doha A. Kattan, Hasanen A. Hammad","doi":"10.28924/2291-8639-21-2023-112","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-112","url":null,"abstract":"The psychological learning theory (PLT) in the formation of moral verdict is represented by the choice-practice paradigm. It involves weighing the effects of various options and choosing one to put into practice. This manuscript is devoted to presenting a general functional equation (FE) for observing animal behavior in such situations. The proposed equation can be used to explain a number of well-known learning and psychological theories. The existence and uniqueness of the solution to a given equation are demonstrated using fixed point (FP) techniques. Furthermore, the stability of the solution to the provided FE is explored in the sense of Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU). Ultimately, to emphasize the importance of our results, two examples are presented.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590366","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：