In the present study, the effect of thermal stratification and heat generation in the boundary layer flow of the Eyring-Powell fluid over the stratified extending surface due to convection has been investigated. The governing equations of the flow are transformed from partial differential equations into a couple of nonlinear ordinary differential equations via similarity variables. The optimal homotopy asymptotic method (OHAM) is used to acquire the approximate analytical solution to the problems. Impacts of flow regulatory parameters on temperature, velocity, skin friction coefficient, and Nusselt number are examined. It is discovered that the fluid velocity augments with a greater value of material parameter E , mixed convection parameter λ , and material fluid parameter σ . The result also revealed that with a higher value of the Prandtl number Pr and the stratified parameter ε , the temperature and the velocity profile decreases, but the opposite behavior is observed when the heat generation/absorption parameter γ increases. The results are compared with available literature and are in good harmony. The present study has substantial ramifications in industrial, engineering, and technological applications, for instance, in designing various chemical processing equipment, distribution of temperature and moisture over agricultural fields, groves of fruit trees, environmental pollution, geothermal reservoirs, thermal insulation, enhanced oil recovery, and underground energy transport.
{"title":"Optimal Homotopy Asymptotic Analysis of the Dynamics of Eyring-Powell Fluid due to Convection Subject to Thermal Stratification and Heat Generation Effect","authors":"Solomon Bati Kejela, Emiru Rufo Adula","doi":"10.1155/2022/6777513","DOIUrl":"https://doi.org/10.1155/2022/6777513","url":null,"abstract":"In the present study, the effect of thermal stratification and heat generation in the boundary layer flow of the Eyring-Powell fluid over the stratified extending surface due to convection has been investigated. The governing equations of the flow are transformed from partial differential equations into a couple of nonlinear ordinary differential equations via similarity variables. The optimal homotopy asymptotic method (OHAM) is used to acquire the approximate analytical solution to the problems. Impacts of flow regulatory parameters on temperature, velocity, skin friction coefficient, and Nusselt number are examined. It is discovered that the fluid velocity augments with a greater value of material parameter \u0000 \u0000 E\u0000 \u0000 , mixed convection parameter \u0000 \u0000 λ\u0000 \u0000 , and material fluid parameter \u0000 \u0000 σ\u0000 \u0000 . The result also revealed that with a higher value of the Prandtl number Pr and the stratified parameter \u0000 \u0000 ε\u0000 \u0000 , the temperature and the velocity profile decreases, but the opposite behavior is observed when the heat generation/absorption parameter \u0000 \u0000 γ\u0000 \u0000 increases. The results are compared with available literature and are in good harmony. The present study has substantial ramifications in industrial, engineering, and technological applications, for instance, in designing various chemical processing equipment, distribution of temperature and moisture over agricultural fields, groves of fruit trees, environmental pollution, geothermal reservoirs, thermal insulation, enhanced oil recovery, and underground energy transport.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48993871","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 obtain some stability results of fixed point sets for a sequence of enriched contraction mappings in the setting of convex metric spaces. In particular, two types of convergence of mappings, namely, G -convergence and H -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation.
{"title":"Stability Results for Enriched Contraction Mappings in Convex Metric Spaces","authors":"Rekha Panicker, Rahul Shukla","doi":"10.1155/2022/5695286","DOIUrl":"https://doi.org/10.1155/2022/5695286","url":null,"abstract":"In this paper, we obtain some stability results of fixed point sets for a sequence of enriched contraction mappings in the setting of convex metric spaces. In particular, two types of convergence of mappings, namely, \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 \u0000 -convergence and \u0000 \u0000 \u0000 \u0000 H\u0000 \u0000 \u0000 \u0000 -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43301656","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, by using properties of attractive points, we study an iteration scheme combining simplified Baillon type and Mann type to find a common fixed point of commutative two nonlinear mappings in Hilbert spaces. Then, we apply the obtained results to prove a new weak convergence theorem.
{"title":"A Weak Convergence Theorem for Common Fixed Points of Two Nonlinear Mappings in Hilbert Spaces","authors":"Takanori Ibaraki, Shunsuke Kajiba, Y. Takeuchi","doi":"10.1155/2022/9568060","DOIUrl":"https://doi.org/10.1155/2022/9568060","url":null,"abstract":"In this paper, by using properties of attractive points, we study an iteration scheme combining simplified Baillon type and Mann type to find a common fixed point of commutative two nonlinear mappings in Hilbert spaces. Then, we apply the obtained results to prove a new weak convergence theorem.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48505141","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, common best proximity point theorems for weakly contractive mapping in b-metric spaces in the cases of nonself-mappings are proved; we introduced the notion of generalized proximal weakly contractive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalized with the references we used.
{"title":"Common Best Proximity Point Theorems for Generalized Proximal Weakly Contractive Mappings in b-Metric Space","authors":"Yohannes Gebru, Yitages Negede","doi":"10.1155/2022/5982401","DOIUrl":"https://doi.org/10.1155/2022/5982401","url":null,"abstract":"In this paper, common best proximity point theorems for weakly contractive mapping in b-metric spaces in the cases of nonself-mappings are proved; we introduced the notion of generalized proximal weakly contractive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalized with the references we used.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45354056","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 examine a family of nonlinear q − difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q − difference operators, recently investigated by the author, and quasilinear Kowalevski type problems that involve contraction q − difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q − Gevrey structure are exhibited. The other feature concerns the problem of confluence of these solutions as q > 1 tends to 1.
{"title":"Asymptotics and Confluence for a Singular Nonlinear \u0000 q\u0000 -Difference-Differential Cauchy Problem","authors":"S. Malek","doi":"10.1155/2022/9637628","DOIUrl":"https://doi.org/10.1155/2022/9637628","url":null,"abstract":"We examine a family of nonlinear \u0000 \u0000 q\u0000 −\u0000 \u0000 difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation \u0000 \u0000 q\u0000 −\u0000 \u0000 difference operators, recently investigated by the author, and quasilinear Kowalevski type problems that involve contraction \u0000 \u0000 q\u0000 −\u0000 \u0000 difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and \u0000 \u0000 q\u0000 −\u0000 \u0000 Gevrey structure are exhibited. The other feature concerns the problem of confluence of these solutions as \u0000 \u0000 q\u0000 >\u0000 1\u0000 \u0000 tends to 1.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44687185","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}
Mohamed Z. Mohamed, Mohammed Yousif, Amjad E. Hamza
In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method’s power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative.
{"title":"Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method","authors":"Mohamed Z. Mohamed, Mohammed Yousif, Amjad E. Hamza","doi":"10.1155/2022/4743234","DOIUrl":"https://doi.org/10.1155/2022/4743234","url":null,"abstract":"In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method’s power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43152373","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 establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle.
本文将galewski - r dulescu非光滑全局隐函数定理推广到无限维Banach空间到欧几里德空间的局部Lipschitz函数。此外，在适当的条件下，我们得到了局部Lipschitz函数的零集参数化的全局隐函数的存在性、唯一性和可能连续性的一系列结果。我们的方法依赖于非光滑临界点理论，该理论基于Ekeland变分原理的推广。
{"title":"On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces","authors":"G. Degla, Cyrille Dansou, Fortuné Dohemeto","doi":"10.1155/2022/1021461","DOIUrl":"https://doi.org/10.1155/2022/1021461","url":null,"abstract":"In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45489944","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 primary aim of this work is to introduce a new class of functions called --pseudo-almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those --pseudo-almost periodic functions including two new composition results which play a crucial role for the existence of some --pseudo-almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the -
{"title":"Measure <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>,</mo>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 ","authors":"James Larrouy, G. N’Guérékata","doi":"10.1155/2022/9558928","DOIUrl":"https://doi.org/10.1155/2022/9558928","url":null,"abstract":"<jats:p>The primary aim of this work is to introduce a new class of functions called <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>μ</mi>\u0000 </math>\u0000 </jats:inline-formula>-<jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>,</mo>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-pseudo-almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>μ</mi>\u0000 </math>\u0000 </jats:inline-formula>-<jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>,</mo>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-pseudo-almost periodic functions including two new composition results which play a crucial role for the existence of some <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>μ</mi>\u0000 </math>\u0000 </jats:inline-formula>-<jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>,</mo>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-pseudo-almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mi>μ</mi>\u0000 </math>\u0000 </jats:inline-formula>-<jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>,</mo>\u0000 <","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46591594","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}
M. Oluwayemi, Sunday Olufemi Olatunji, T. Ogunlade
Beta function has some applications in differential equations and other areas of sciences and engineering where certain definite integrals are used. However, its applications to univalent functions have not been explored based on the available literature. In this work, therefore, the authors defined a univalent function associated with the beta function B m , n with m , n > 0 . Some geometric properties of the function are discussed.
函数在微分方程和其他科学和工程领域中有一些应用，其中使用了一定的定积分。然而，在现有文献的基础上，尚未对其在单价函数中的应用进行探讨。因此，在这项工作中，作者定义了一个与β函数B m, n with m, n >0 0相关的一元函数。讨论了该函数的一些几何性质。
{"title":"On Certain Properties of a Univalent Function Associated with Beta Function","authors":"M. Oluwayemi, Sunday Olufemi Olatunji, T. Ogunlade","doi":"10.1155/2022/8150057","DOIUrl":"https://doi.org/10.1155/2022/8150057","url":null,"abstract":"Beta function has some applications in differential equations and other areas of sciences and engineering where certain definite integrals are used. However, its applications to univalent functions have not been explored based on the available literature. In this work, therefore, the authors defined a univalent function associated with the beta function \u0000 \u0000 B\u0000 \u0000 \u0000 m\u0000 ,\u0000 n\u0000 \u0000 \u0000 \u0000 with \u0000 \u0000 m\u0000 ,\u0000 n\u0000 >\u0000 0\u0000 \u0000 . Some geometric properties of the function are discussed.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45257600","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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