In this article, a numerical scheme is proposed to solve a class of time-fractional stochastic delay differential equations (TFSDDEs) with fractional Brownian motion (fBm). First, we convert the TFSDDE into a non-delay equation by using a step-by-step scheme. Then, by applying a collocation method based on Jacobi polynomials (JPs) in each step, the non-delay equation is reduced to a nonlinear system of algebraic equations. The convergence analysis of the presented scheme is evaluated. Finally, two numerical test examples are presented to highlight the applicability and efficiency of the investigated method.
{"title":"Numerical solution for a class of time-fractional stochastic delay differential equation with fractional Brownian motion","authors":"S. Banihashemi, H. Jafari, A. Babaei","doi":"10.30495/JME.V15I0.2076","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2076","url":null,"abstract":"In this article, a numerical scheme is proposed to solve a class of time-fractional stochastic delay differential equations (TFSDDEs) with fractional Brownian motion (fBm). First, we convert the TFSDDE into a non-delay equation by using a step-by-step scheme. Then, by applying a collocation method based on Jacobi polynomials (JPs) in each step, the non-delay equation is reduced to a nonlinear system of algebraic equations. The convergence analysis of the presented scheme is evaluated. Finally, two numerical test examples are presented to highlight the applicability and efficiency of the investigated method.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48797189","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}
The aim of this research is to define $bot$-proximally increasing mapping and obtain several best proximity point results concerning this mapping in the framework of new spaces, which is called orthogonal $b$-metric spaces. Also, several well-known fixed point results in such spaces are established. All main results and new definitions are supported by some illustrative and interesting examples.
{"title":"Orthogonal $b$-metric spaces and best proximity points","authors":"K. Fallahi, S. Eivani","doi":"10.30495/JME.V0I0.2000","DOIUrl":"https://doi.org/10.30495/JME.V0I0.2000","url":null,"abstract":"The aim of this research is to define $bot$-proximally increasing mapping and obtain several best proximity point results concerning this mapping in the framework of new spaces, which is called orthogonal $b$-metric spaces. Also, several well-known fixed point results in such spaces are established. All main results and new definitions are supported by some illustrative and interesting examples.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44507408","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}
This paper deals with some qualitative properties of a class of nonlinear singular systems with multiple constant delays. Via the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB software. By this work, we extend and improve some results of the past literature.
{"title":"On qualitative behaviors of nonlinear singular systems with multiple constant delays","authors":"C. Tunç, A. Yiğit","doi":"10.30495/JME.V16I0.2018","DOIUrl":"https://doi.org/10.30495/JME.V16I0.2018","url":null,"abstract":"This paper deals with some qualitative properties of a class of nonlinear singular systems with multiple constant delays. Via the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB software. By this work, we extend and improve some results of the past literature.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42751725","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}
In this paper the problem of hypothesis testing is consid-ered as an estimation problem within a decision-theoretic framework forestimating the accuracy of the test. The usual p-value is an admissi-ble estimator for the one-sided testing of the scale parameter under thesquared error loss function in the Pareto distribution. In the presence ofnuisance parameter for model, the generalized p-value is inadmissible.Even though the usual p-value and the generalized p-value are inadmis-sible estimators for the one-sided testing of the shape parameter, it isdicult to exhibit a better estimator than the usual p-value. For thetwo-sided testing, although the usual p-value is generally inadmissible, ithas been shown that the usual p-value as an estimator for the two-sidedtesting of the shape parameter may not be too bad.
{"title":"The admissibility of the p-value for the testing of parameters in the Pareto distribution","authors":"F. Hormozinejad, Masoumeh Babadi, A. Zaherzadeh","doi":"10.30495/JME.V0I0.1843","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1843","url":null,"abstract":"In this paper the problem of hypothesis testing is consid-ered as an estimation problem within a decision-theoretic framework forestimating the accuracy of the test. The usual p-value is an admissi-ble estimator for the one-sided testing of the scale parameter under thesquared error loss function in the Pareto distribution. In the presence ofnuisance parameter for model, the generalized p-value is inadmissible.Even though the usual p-value and the generalized p-value are inadmis-sible estimators for the one-sided testing of the shape parameter, it isdicult to exhibit a better estimator than the usual p-value. For thetwo-sided testing, although the usual p-value is generally inadmissible, ithas been shown that the usual p-value as an estimator for the two-sidedtesting of the shape parameter may not be too bad.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44509910","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}
The objective of this paper is to investigate, by applying the standard Caputo fractional $q$--derivative of order $alpha$, the existence of solutions for the singular fractional $q$--integro-differential equation $mathcal{D}_q^alpha [k](t) = Omega (t , k(t), k'(t), mathcal{D}_q^beta [k](t), int_0^t f(r) k(r) , {mathrm d}r )$, under some boundary conditions where $Omega(t, k_1, k_2, k_3, k_4)$ is singular at some point $0 leq tleq 1$, on a time scale $mathbb{T}_{ t_0} = { t : t =t_0q^n}cup {0}$, for $nin mathbb{N}$ where $t_0 in mathbb{R}$ and $q in (0,1)$. We consider the compact map and avail the Lebesgue dominated theorem for finding solutions of the addressed problem. Besides, we prove the main results in context of completely continuous functions. Our attention is concentrated on fractional multi-step methods of both implicit and explicit type, for which sufficient existence conditions are investigated. Lastly, we present some examples involving graphs, tables and algorithms to illustrate the validity of our theoretical findings.
{"title":"To investigate a class of the singular fractional integro-differential quantum equations with multi-step methods","authors":"M. Samei, Hasti Zanganeh, S. M. Aydoǧan","doi":"10.30495/JME.V15I0.2070","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2070","url":null,"abstract":"The objective of this paper is to investigate, by applying the standard Caputo fractional $q$--derivative of order $alpha$, the existence of solutions for the singular fractional $q$--integro-differential equation $mathcal{D}_q^alpha [k](t) = Omega (t , k(t), k'(t), mathcal{D}_q^beta [k](t), int_0^t f(r) k(r) , {mathrm d}r )$, under some boundary conditions where $Omega(t, k_1, k_2, k_3, k_4)$ is singular at some point $0 leq tleq 1$, on a time scale $mathbb{T}_{ t_0} = { t : t =t_0q^n}cup {0}$, for $nin mathbb{N}$ where $t_0 in mathbb{R}$ and $q in (0,1)$. We consider the compact map and avail the Lebesgue dominated theorem for finding solutions of the addressed problem. Besides, we prove the main results in context of completely continuous functions. Our attention is concentrated on fractional multi-step methods of both implicit and explicit type, for which sufficient existence conditions are investigated. Lastly, we present some examples involving graphs, tables and algorithms to illustrate the validity of our theoretical findings.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46776488","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}
The most significant objective of this article is the adoption of a method with a free parameter known as “The Optimum Asymptotic Homotopy Method” which has been utilized in order to obtain answers for integral differential equations of high-order non integer derivative.The process in this method is more favorable than “Homotopy Perturbation Method” as it has a more rapid convergence compared to the mentioned method or even the similar methods. Another advantage of this method is that the convergence rate is recognized as control area. It is worth mentioning that Caputo derivative is adopted in this article.A number of instances are provided to better understand the method and its level of efficiency compared to other same methods.
{"title":"Approximate solution for high order fractional integro-differential equations via an optimum parameter method","authors":"B. Agheli, R. Darzi, A. Dabbaghian","doi":"10.30495/JME.V15I0.2081","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2081","url":null,"abstract":"The most significant objective of this article is the adoption of a method with a free parameter known as “The Optimum Asymptotic Homotopy Method” which has been utilized in order to obtain answers for integral differential equations of high-order non integer derivative.The process in this method is more favorable than “Homotopy Perturbation Method” as it has a more rapid convergence compared to the mentioned method or even the similar methods. Another advantage of this method is that the convergence rate is recognized as control area. It is worth mentioning that Caputo derivative is adopted in this article.A number of instances are provided to better understand the method and its level of efficiency compared to other same methods.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49298779","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}
In this paper, we formulate a numerical method to approximate the solution of non-linear fractal-fractional Burgers equation. In this model, differential operators are defined in the Atangana-Riemann-Liouville sense with Mittage-Leffler kernel. We first expand the spatial derivatives using barycentric interpolation method and then we derive an operational matrix (OM) of the fractal-fractional derivative for the Legendre polynomials. To be more precise, two approximation tools are coupled to convert the fractal-fractional Burgers equation into a system of algebraic equations which is technically uncomplicated and can be solved using available mathematical software such as MATLAB. To investigate the agreement between exact and approximate solutions, several examples are examined.
{"title":"Barycentric Legendre interpolation method for solving nonlinear fractal-fractional Burgers equation","authors":"A. Rezazadeh, A. M. Nagy, Z. Avazzadeh","doi":"10.30495/JME.V15I0.2009","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2009","url":null,"abstract":"In this paper, we formulate a numerical method to approximate the solution of non-linear fractal-fractional Burgers equation. In this model, differential operators are defined in the Atangana-Riemann-Liouville sense with Mittage-Leffler kernel. We first expand the spatial derivatives using barycentric interpolation method and then we derive an operational matrix (OM) of the fractal-fractional derivative for the Legendre polynomials. To be more precise, two approximation tools are coupled to convert the fractal-fractional Burgers equation into a system of algebraic equations which is technically uncomplicated and can be solved using available mathematical software such as MATLAB. To investigate the agreement between exact and approximate solutions, several examples are examined.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45219442","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}
We provide criteria for identifying exact pairs of zero-divisors from zero-divisor graphs of commutative rings, and extend these criteria to compressed zero-divisor graphs. Finally, our results are translated as constructions for exact zero-divisor subgraphs.
{"title":"Identifying Exact Pairs of Zero-divisors from Zero-divisor Graphs of Commutative Rings","authors":"Justin Hoffmeier","doi":"10.30495/JME.V0I0.1834","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1834","url":null,"abstract":"We provide criteria for identifying exact pairs of zero-divisors from zero-divisor graphs of commutative rings, and extend these criteria to compressed zero-divisor graphs. Finally, our results are translated as constructions for exact zero-divisor subgraphs.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47086459","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}
In this research work, we proposed a new fractional numer-ical algorithm to obtain the exact solutions of generalized fractional-order dierential equations in Caputo sense of order 0 < beta< 1. Fornding the exact solutions by the proposed technique we used the solu-tions of integer-order dierential equations. Generalization of the pro-posed scheme to nite systems is also introduced. At the last, we gave some numerical simulations of some specic equations along with thesolution of a computer virus model to illustrate the applications of ourresults.
{"title":"A new technique to solve generalized Caputo type fractional differential equations with the example of computer virus model","authors":"Pushpendra Kumar, V. S. Erturk, Anoop Kumar","doi":"10.30495/JME.V15I0.2052","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2052","url":null,"abstract":"In this research work, we proposed a new fractional numer-ical algorithm to obtain the exact solutions of generalized fractional-order dierential equations in Caputo sense of order 0 < beta< 1. Fornding the exact solutions by the proposed technique we used the solu-tions of integer-order dierential equations. Generalization of the pro-posed scheme to nite systems is also introduced. At the last, we gave some numerical simulations of some specic equations along with thesolution of a computer virus model to illustrate the applications of ourresults.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42243967","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}
In this paper, we shell generalize concave operators to multifunction versions. Then we obtain some fixed point results for such multifunctions in partially ordered spaces.
本文将凹算子推广到多函数形式。然后我们得到了偏序空间中这类多函数的一些不动点结果。
{"title":"Concave Multifunctions and the Hammerstein Integral inclusion Problem","authors":"R. Haghi, Hadi Hadavi","doi":"10.30495/JME.V15I0.2045","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2045","url":null,"abstract":"In this paper, we shell generalize concave operators to multifunction versions. Then we obtain some fixed point results for such multifunctions in partially ordered spaces.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48501539","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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