This paper establishes a study on some important latest innovations in the existence and uniqueness results by means of Banach contraction fixed point theorem for Caputo fractional Volterra-Fredholm integro-differential equations with boundary condition. New conditions on the nonlinear terms are given to pledge the equivalence. Finally, an illustrative example is also presented.
{"title":"EXISTENCE AND UNIQUENESS RESULTS FOR VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS","authors":"Ahmed A. Hamoud, N. M. Mohammed, K. Ghadle","doi":"10.31197/atnaa.703984","DOIUrl":"https://doi.org/10.31197/atnaa.703984","url":null,"abstract":"This paper establishes a study on some important latest innovations in the existence and uniqueness results by means of Banach contraction fixed point theorem for Caputo fractional Volterra-Fredholm integro-differential equations with boundary condition. New conditions on the nonlinear terms are given to pledge the equivalence. Finally, an illustrative example is also presented.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"13 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79345249","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}
T. Abdeljawad, Q. Al‐Mdallal, Z. Hammouch, F. Jarad
The literature reveals that numerous real-life phenomena in the subjects of physics and engineering which are governed by highly nonlinear Partial differential equations (PDEs) with unknown analytical solutions. More precisely, the (PDEs) arise in a wide variety of physical problems such as; by way of example not exhaustive enumeration, fluid dynamics, engineering mathematics, electrostatics, plasma physics, solid mechanics, chemistry, quantum field theory, bio-mathematics, etc. Therefore, such (PDEs) have received a huge attention from mathematicians, physicists, and engineers for the sake of approximating their analytical solutions.
{"title":"A Special Issue:Recent Developments in Nonlinear Partial Differential Equations","authors":"T. Abdeljawad, Q. Al‐Mdallal, Z. Hammouch, F. Jarad","doi":"10.31197/atnaa.810371","DOIUrl":"https://doi.org/10.31197/atnaa.810371","url":null,"abstract":"The literature reveals that numerous real-life phenomena in the subjects of physics and engineering which are governed by highly nonlinear Partial differential equations (PDEs) with unknown analytical solutions. More precisely, the (PDEs) arise in a wide variety of physical problems such as; by way of example not exhaustive enumeration, fluid dynamics, engineering mathematics, electrostatics, plasma physics, solid mechanics, chemistry, quantum field theory, bio-mathematics, etc. Therefore, such (PDEs) have received a huge attention from mathematicians, physicists, and engineers for the sake of approximating their analytical solutions.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75966193","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}
Abdelkrim Salim, M. Benchohra, J. Lazreg, J. Henderson
In the present article, we prove some results concerning the existence of solutions for a class of initial value problem for nonlinear implicit fractional di erential equations with non-instantaneous impulses and generalized Hilfer fractional derivative in Banach spaces. The results are based on xed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. An example is included to show the applicability of our results.
{"title":"Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Non-Instantaneous Impulses in Banach Spaces","authors":"Abdelkrim Salim, M. Benchohra, J. Lazreg, J. Henderson","doi":"10.31197/atnaa.825294","DOIUrl":"https://doi.org/10.31197/atnaa.825294","url":null,"abstract":"In the present article, we prove some results concerning the existence of solutions for a class of initial value problem for nonlinear implicit fractional di erential equations with non-instantaneous impulses and generalized Hilfer fractional derivative in Banach spaces. The results are based on xed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. An example is included to show the applicability of our results.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"2014 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86502489","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 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder xed point theorem to multimaps on non-compact convex sets. Since then several groups of the L-space theorists introduced coercivity families and applied them to L-spaces, H-spaces, etc. In this article, we show that better forms of such works can be deduced from a general KKM theorem on abstract convex spaces in our previous works. Consequently, all of known KKM theoretic results on L-spaces related coercivity families are extended to corresponding better forms on abstract convex spaces. This article is a continuation of our [38] and a revised and extended version of [34].
2005年，Ben-El-Mechaiekh, Chebbi, and Florenzano推广了Ky Fan 1984年关于拓扑向量空间中非紧凸集上一组闭集交点的KKM定理。他们还将Fan-Browder杂点定理推广到非紧凸集上的多映射。从那时起，一些l空间理论家引入了矫顽力族，并将它们应用于l空间、h空间等。在本文中，我们证明了这些作品的更好形式可以从抽象凸空间上的一般KKM定理中推导出来。因此，所有已知的关于l空间的矫顽力族的KKM理论结果推广到抽象凸空间上相应的更好形式。本文是文献[38]的延续，是文献[34]的修订扩展版。
{"title":"The rise and fall of L-spaces, II","authors":"Sehie Park","doi":"10.31197/atnaa.847835","DOIUrl":"https://doi.org/10.31197/atnaa.847835","url":null,"abstract":"In 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder xed point theorem to multimaps on non-compact convex sets. Since then several groups of the L-space theorists introduced coercivity families and applied them to L-spaces, H-spaces, etc. In this article, we show that better forms of such works can be deduced from a general KKM theorem on abstract convex spaces in our previous works. Consequently, all of known KKM theoretic results on L-spaces related coercivity families are extended to corresponding better forms on abstract convex spaces. This article is a continuation of our [38] and a revised and extended version of [34].","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83083222","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 Study, an accurate method for summing the general Dirichlet series is presented. Long range terms of this series are calculated by a multilevel approach. The Dirichlet series, in this technique, is decomposed into two parts, a local part and a smooth part. The local part vanishes beyond some cut off distance, "$r_0$", and it can be cheaply computed . The complexity of calculations depends on $r_0$. The smooth part is calculated on a sequence of grids with increasing meshsize. Treating the smooth part using multilevels of grid points overcomes the high cost of calculating the long range terms. A high accuracy in approximating the smooth part is obtained with the same complexity of computing the local part. The method is tested on the Riemann Zeta function. Since there is no closed form for this function with odd integer orders, the method is applied for orders $s= 3, 5, 7,$ and $9$. In comparison with the direct calculations, remarkable results are obtained for $s=3$ and $s=5$; the reason is the major effect of the long range terms. For $s=7,$ and $s=9$, results obtained are better than those of direct calculations. The method is compared with efficient well known methods. The comparison shows the superiority of the multilevel method.
{"title":"Multilevel Evaluation of the General Dirichlet Series","authors":"I. Suwan","doi":"10.31197/atnaa.810766","DOIUrl":"https://doi.org/10.31197/atnaa.810766","url":null,"abstract":"In this Study, an accurate method for summing the general Dirichlet series is presented. Long range terms of this series are calculated by a multilevel approach. The Dirichlet series, in this technique, is decomposed into two parts, a local part and a smooth part. The local part vanishes beyond some cut off distance, \"$r_0$\", and it can be cheaply computed . The complexity of calculations depends on $r_0$. The smooth part is calculated on a sequence of grids with increasing meshsize. Treating the smooth part using multilevels of grid points overcomes the high cost of calculating the long range terms. A high accuracy in approximating the smooth part is obtained with the same complexity of computing the local part. The method is tested on the Riemann Zeta function. Since there is no closed form for this function with odd integer orders, the method is applied for orders $s= 3, 5, 7,$ and $9$. In comparison with the direct calculations, remarkable results are obtained for $s=3$ and $s=5$; the reason is the major effect of the long range terms. For $s=7,$ and $s=9$, results obtained are better than those of direct calculations. The method is compared with efficient well known methods. The comparison shows the superiority of the multilevel method.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86212864","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}
Enzymatic inhibition is one of the key regulatory mechanisms in cellular metabolism, especially the enzymatic competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we derive a mathematical model describing the enzymatic competitive inhibition by product. The model consists of a coupled system of nonlinear ordinary differential equations for the species of interest. Using nondimensionalization analysis, a formula for product formation rate for this mechanism is obtained in a transparent manner. Further analysis for this formula yields qualitative insights into the maximal reaction velocity and apparent Michaelis-Menten constant. Integrating the model numerically, the effects of the model parameters on the model output are also investigated. Finally, a potential application of the model to realistic enzymes is briefly discussed.
{"title":"Numerical analysis of coupled systems of ODEs and applications to enzymatic competitive inhibition by product","authors":"V. Mai, T. Nhan","doi":"10.31197/ATNAA.820590","DOIUrl":"https://doi.org/10.31197/ATNAA.820590","url":null,"abstract":"Enzymatic inhibition is one of the key regulatory mechanisms in cellular metabolism, especially the enzymatic competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we derive a mathematical model describing the enzymatic competitive inhibition by product. The model consists of a coupled system of nonlinear ordinary differential equations for the species of interest. Using nondimensionalization analysis, a formula for product formation rate for this mechanism is obtained in a transparent manner. Further analysis for this formula yields qualitative insights into the maximal reaction velocity and apparent Michaelis-Menten constant. Integrating the model numerically, the effects of the model parameters on the model output are also investigated. Finally, a potential application of the model to realistic enzymes is briefly discussed.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78549780","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}
K. Jangid, Sunil Dutt Prohit, K. Nisar, T. Abdeljawad
The principal aim of this article is to establish certain generalized fractional integral inequalities by utilizing the Marichev-Saigo-Maeda (MSM) fractional integral operator. Some new classes of generalized fractional integral inequalities for a class of n (n ∈ $mathbb{N}$) positive continuous and decreasing functions on [a, b] by using the MSM fractional integral operator also derived.
{"title":"Certain Generalized Fractional Integral Inequalities","authors":"K. Jangid, Sunil Dutt Prohit, K. Nisar, T. Abdeljawad","doi":"10.31197/ATNAA.775089","DOIUrl":"https://doi.org/10.31197/ATNAA.775089","url":null,"abstract":"The principal aim of this article is to establish certain generalized fractional integral inequalities by utilizing the Marichev-Saigo-Maeda (MSM) fractional integral operator. Some new classes of generalized fractional integral inequalities for a class of n (n ∈ $mathbb{N}$) positive continuous and decreasing functions on [a, b] by using the MSM fractional integral operator also derived.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78769849","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}
Abdelilah Lamrani Alaoui, E. Azroul, Abdelouahed Alla Hamou
In this paper, the existence and uniqueness of the weak solution for a linear parabolic equation with conformable derivative are proved, the existence of weak periodic solutions for conformable fractional parabolic nonlinear differential equation is proved by using a more generalized monotone iterative method combined with the method of upper and lower solutions. We prove the monotone sequence converge to weak periodic minimal and maximal solutions. Moreover, the conformable version of the Lions-Magness and Aubin–Lions lemmas are also proved.
{"title":"Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems","authors":"Abdelilah Lamrani Alaoui, E. Azroul, Abdelouahed Alla Hamou","doi":"10.31197/atnaa.770669","DOIUrl":"https://doi.org/10.31197/atnaa.770669","url":null,"abstract":"In this paper, the existence and uniqueness of the weak solution for a linear parabolic equation with conformable derivative are proved, the existence of weak periodic solutions for conformable fractional parabolic nonlinear differential equation is proved by using a more generalized monotone iterative method combined with the method of upper and lower solutions. We prove the monotone sequence converge to weak periodic minimal and maximal solutions. Moreover, the conformable version of the Lions-Magness and Aubin–Lions lemmas are also proved.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85424097","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 the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms in terms of the Hessenberg determinants and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers. This preprint has been formally published as "Feng Qi, Muhammet Cihat Dagli, and Wei-Shih Du, Determinantal forms and recursive relations of the Delannoy two-functional sequence, Advances in the Theory of Nonlinear Analysis and its Applications, vol. 4, no. 3, pp. 184--193 (2020); available online at https://doi.org/10.31197/atnaa.772734."
{"title":"Determinantal forms and recursive relations of the Delannoy two-functional sequence","authors":"Feng Qi (祁锋), M. C. Dağlı, Wei-Shih Du","doi":"10.31219/osf.io/u683y","DOIUrl":"https://doi.org/10.31219/osf.io/u683y","url":null,"abstract":"In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms in terms of the Hessenberg determinants and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers. This preprint has been formally published as \"Feng Qi, Muhammet Cihat Dagli, and Wei-Shih Du, Determinantal forms and recursive relations of the Delannoy two-functional sequence, Advances in the Theory of Nonlinear Analysis and its Applications, vol. 4, no. 3, pp. 184--193 (2020); available online at https://doi.org/10.31197/atnaa.772734.\"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89021371","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 introduce the notion of $F$-contraction in the setting of complete metric space and we prove a fixed point theorem for $F$-contractive iteration.
本文在完备度量空间中引入了$F$-收缩的概念，并证明了$F$-收缩迭代的不动点定理。
{"title":"A fixed point theorem for mappings with a F-contractive iterate","authors":"A. Öztürk","doi":"10.31197/atnaa.644325","DOIUrl":"https://doi.org/10.31197/atnaa.644325","url":null,"abstract":"In this paper, we introduce the notion of $F$-contraction in the setting of complete metric space and we prove a fixed point theorem for $F$-contractive iteration.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87460867","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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