The Sturm-Liouville fraction equations have considerable role applications in some different phenomena such as mechanical and electrical engineering, medicine and physics. Thus, it is better we review different versions of this equation. We study a $k$-dimensional system of Sturm-Liouville hybrid equations y using the $alpha$-admissible method. We investigate the existence of solutions for the $k$-dimensional system of hybrid equations with some multi-point boundary value conditions. We provide an example to illustrate our main result.
{"title":"On a $k$-dimensional system of hybrid fractional differential equations with multi-point boundary conditions","authors":"S. M. Aydoǧan","doi":"10.30495/JME.V15I0.2065","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2065","url":null,"abstract":"The Sturm-Liouville fraction equations have considerable role applications in some different phenomena such as mechanical and electrical engineering, medicine and physics. Thus, it is better we review different versions of this equation. We study a $k$-dimensional system of Sturm-Liouville hybrid equations y using the $alpha$-admissible method. We investigate the existence of solutions for the $k$-dimensional system of hybrid equations with some multi-point boundary value conditions. We provide an example to illustrate our main result.","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":"49642614","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}
Looking for offer a solution of the Riccati's differential equations of fractional order (FRDEs) involving Caputo derivative (CD), Caputo-Fabrizio derivative (CFD) or Atangana-Baleanu derivative (ABD) in this comparative research is based on a semi-analytical iterative approach. Temimi and Ansari introduced this method and called it TAM. The comparison of the time used in minutes is given for three derivatives CD, CFD and ABD. Meanwhile, the comparison of the approximate solutions with CD, CFD and ABD are presented. Regarding the help of the software Mathematica, all the results have been obtained and the calculations have been done.
{"title":"A semi-analytical solutions of fractional Riccati's differential equation via singular and non-singular operators","authors":"Mohammad Adabitabar Firozja, B. Agheli","doi":"10.30495/JME.V15I0.1917","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1917","url":null,"abstract":"Looking for offer a solution of the Riccati's differential equations of fractional order (FRDEs) involving Caputo derivative (CD), Caputo-Fabrizio derivative (CFD) or Atangana-Baleanu derivative (ABD) in this comparative research is based on a semi-analytical iterative approach. Temimi and Ansari introduced this method and called it TAM. The comparison of the time used in minutes is given for three derivatives CD, CFD and ABD. Meanwhile, the comparison of the approximate solutions with CD, CFD and ABD are presented. Regarding the help of the software Mathematica, all the results have been obtained and the calculations have been done.","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":"48040988","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}
H. Mesgarani, Masod Bakhshandeh, Yones Esmaeelzade
In this paper, the temporal fractional Black–Scholes model (TFBSM) is discussed in the limited specific domain which the time derivative of this template is the Caputo fractional function. The value variance of the associated fractal transmission method was applied to forecast TFBSM. For solving, at first the semi-discrete scheme is obtained by using linear interpolation with a temporally $tau^{2-alpha}$ order accuracy. Then, the full scheme is collected by approximating the spatial derivative terms by helping the Chebyshev collocation system focused on the fourth form. Finally, the unconditional stability and convergence order is evaluated by performing the energy process. As an implementation of this method, two examples of the TFBSM was reported to demonstrate the accuracy of the developed scheme. Calculation simulation and comparison show that the suggested strategy is very accurate and effective.
{"title":"The stability and convergence of the numerical computation for the temporal fractional Black–Scholes equation","authors":"H. Mesgarani, Masod Bakhshandeh, Yones Esmaeelzade","doi":"10.30495/JME.V15I0.1991","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1991","url":null,"abstract":"In this paper, the temporal fractional Black–Scholes model (TFBSM) is discussed in the limited specific domain which the time derivative of this template is the Caputo fractional function. The value variance of the associated fractal transmission method was applied to forecast TFBSM. For solving, at first the semi-discrete scheme is obtained by using linear interpolation with a temporally $tau^{2-alpha}$ order accuracy. Then, the full scheme is collected by approximating the spatial derivative terms by helping the Chebyshev collocation system focused on the fourth form. Finally, the unconditional stability and convergence order is evaluated by performing the energy process. As an implementation of this method, two examples of the TFBSM was reported to demonstrate the accuracy of the developed scheme. Calculation simulation and comparison show that the suggested strategy is very accurate and effective.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47462059","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}
An effective modified of the Picard iteration method ( PIM ) is presented for solving the linear and nonlinear fractional optimal control problems ( FOCP ) in the Caputo sense. Here, the control function is first approximated by a finite series with unknown coefficients. Then the modified PIM is utilized to simulate the resulting fractional equations. Finally, the unknown coefficients could be computed by applying an optimization procedure. Some test examples are given to show the accuracy and validity of the method.
{"title":"A modified Picard iteration method to solve fractional optimal control problems","authors":"A. Ghorbani","doi":"10.30495/JME.V15I0.1971","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1971","url":null,"abstract":"An effective modified of the Picard iteration method ( PIM ) is presented for solving the linear and nonlinear fractional optimal control problems ( FOCP ) in the Caputo sense. Here, the control function is first approximated by a finite series with unknown coefficients. Then the modified PIM is utilized to simulate the resulting fractional equations. Finally, the unknown coefficients could be computed by applying an optimization procedure. Some test examples are given to show the accuracy and validity of the method.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48594662","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 seeks to investigate the existence and uniqueness of solutions to fuzzy differential equations driven by Liu's process. To this end, we provide andprove a novel existence and uniqueness theorem for fuzzy differential equations under Local Lipschitz and monotone conditions. This result allows us to consider and analyze solutions to a wide range of nonlinear fuzzy differential equations driven by Liu's process. To illustrate the main advantage of the approach some examples are finally given.
{"title":"On the Existence and Uniqueness of Fuzzy Differential Equations with Monotone Condition","authors":"N. Ahmady, Samira Siah mansori, M. Gachpazan","doi":"10.30495/JME.V0I0.1752","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1752","url":null,"abstract":"This paper seeks to investigate the existence and uniqueness of solutions to fuzzy differential equations driven by Liu's process. To this end, we provide andprove a novel existence and uniqueness theorem for fuzzy differential equations under Local Lipschitz and monotone conditions. This result allows us to consider and analyze solutions to a wide range of nonlinear fuzzy differential equations driven by Liu's process. To illustrate the main advantage of the approach some examples are finally given.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44084802","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}
Here we study the existence and multiplicity of solutions for the following fractional problem $$ (-Delta)_p^s u+a(x) |u|^{p-2} u= f(x,u), $$ with the Dirichlet boundary condition $u=0$ on $partialOmega$ where $Omega$ is a bounded domain with smooth boundary, $pgeq 2$, $sin(0,1)$ and $a(x)$ is a sign-changing function. Moreover, we consider two different assumptions on the function $f(x,u)$, including the cases of nonnegative and sign-changing function.
{"title":"Existence of solution for a class of fractional problems with sign-changing functions","authors":"F. M. Yaghoobi, J. Shamshiri","doi":"10.30495/JME.V15I0.2008","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2008","url":null,"abstract":"Here we study the existence and multiplicity of solutions for the following fractional problem $$ (-Delta)_p^s u+a(x) |u|^{p-2} u= f(x,u), $$ with the Dirichlet boundary condition $u=0$ on $partialOmega$ where $Omega$ is a bounded domain with smooth boundary, $pgeq 2$, $sin(0,1)$ and $a(x)$ is a sign-changing function. Moreover, we consider two different assumptions on the function $f(x,u)$, including the cases of nonnegative and sign-changing function.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47474474","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}
Theory of zeta functions and fractional calculus plays an important role in the statistical problems and Shannon's entropy. Estimation of Shannon's entropies of information sources from numerical simulation of long orbits is difficult. Our aim within this paper is to present a strong upper bound for the Shannon's entropy of information sources.
{"title":"An improvement of the upper bound on the entropy of information sources","authors":"Y. Sayyari","doi":"10.30495/JME.V15I0.1976","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1976","url":null,"abstract":"Theory of zeta functions and fractional calculus plays an important role in the statistical problems and Shannon's entropy. Estimation of Shannon's entropies of information sources from numerical simulation of long orbits is difficult. Our aim within this paper is to present a strong upper bound for the Shannon's entropy of information sources.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43285088","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}
S. Datta, S. Sarkar, G. Chakraborty, Arghyatanu Manna
Let be a transcendental entire function defined in the open complex plane ℂ. A difference-monomial generated by . Now for the sake of definiteness let us take a difference-polynomial generated by . In this paper we compare the Valiron defect with the relative Nevanlinna defect of a particular type of differential-difference polynomial generated by a transcendental entire function with respect to integrated moduli of logarithmic derivative. Some examples are provided in order to justify the results obtained.
{"title":"On relative deficiencies of difference polynomials from the view point of integrated moduli of logarithmic derivative","authors":"S. Datta, S. Sarkar, G. Chakraborty, Arghyatanu Manna","doi":"10.30495/JME.V0I0.1726","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1726","url":null,"abstract":"Let be a transcendental entire function defined in the open complex plane ℂ. A difference-monomial generated by . Now for the sake of definiteness let us take a difference-polynomial generated by . In this paper we compare the Valiron defect with the relative Nevanlinna defect of a particular type of differential-difference polynomial generated by a transcendental entire function with respect to integrated moduli of logarithmic derivative. Some examples are provided in order to justify the results obtained.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43155310","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}
Just like estimating cost efficiency in the usual DEA, it is important to calculate cost efficiency in DMUs with the DEA network. In the existing models, it is assumed that the input prices are the same for all the DMUs. The present paper is aimed to introduce a model for cost efficiency evaluation in DMUs with network structure with different input prices. Subsequently, the proposed network cost efficiency will be decomposed into network allocative, price, and technical efficiencies.
{"title":"Cost Efficiency Estimation in Network DEA in the Case of Varying Input Prices","authors":"Masoomeh Hajiani, R. Fallahnejad","doi":"10.30495/JME.V0I0.1467","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1467","url":null,"abstract":"Just like estimating cost efficiency in the usual DEA, it is important to calculate cost efficiency in DMUs with the DEA network. In the existing models, it is assumed that the input prices are the same for all the DMUs. The present paper is aimed to introduce a model for cost efficiency evaluation in DMUs with network structure with different input prices. Subsequently, the proposed network cost efficiency will be decomposed into network allocative, price, and technical efficiencies.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42705351","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}
Let G be a graph with n vertices and m edges. The min-imum edge dominating energy is dened as the sum of the absolutevalues of eigenvalues of the minimum edge dominating matrix of thegraph G. In this paper, some lower and upper bounds for the minimumedge dominating energy of the graph G are established.
{"title":"New results on the minimum edge dominating energy of a graph","authors":"F. Movahedi, M. Akhbari","doi":"10.30495/JME.V0I0.1627","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1627","url":null,"abstract":"Let G be a graph with n vertices and m edges. The min-imum edge dominating energy is dened as the sum of the absolutevalues of eigenvalues of the minimum edge dominating matrix of thegraph G. In this paper, some lower and upper bounds for the minimumedge dominating energy of the graph G are established.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"61 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70077026","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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