I. Zari, T. Gul, K. Dosmagulova, T. Khan, Safia Haq
The present work investigates the impacts of the Lorentz forces, porosity factor, viscous dissipation and radiation in thermo-Marangoni convective flow of a nanofluids (comprising two distinct kinds of carbon nanotubes ($CNT_{s}$)), in water ($H_{2}O$). Heat transportation developed by Marangoni forces happens regularly in microgravity situations, heat pipes, and in crystal growth. Therefore, Marangoni convection is considered in the flow model. A nonlinear system is constructed utilizing these assumptions which further converted to ordinary differential equations (ODEs) by accurate similarity transformations. The homotopic scheme is utilized to compute the exact solution for the proposed system. The study reveals that higher estimations of Hartmann number and Marangoni parameter speed up the fluid velocity while the opposite behavior is noted for porosity factor. Further, the rate of heat transfer shows upward trend for the Hartmann number, Marangoni parameter, nanoparticle solid volume fraction, radiation parameter whereas a downward trend is followed by the Brinkman number and porosity factor. It is fascinating to take observe that contemporary analytical outcomes validate the superb convergence with previous investigation.
{"title":"Heat transfer analysis of Radiative-Marangoni Convective flow in nanofluid comprising Lorentz forces and porosity effects","authors":"I. Zari, T. Gul, K. Dosmagulova, T. Khan, Safia Haq","doi":"10.31197/atnaa.1187342","DOIUrl":"https://doi.org/10.31197/atnaa.1187342","url":null,"abstract":"The present work investigates the impacts of the Lorentz forces, porosity factor, viscous dissipation and radiation in thermo-Marangoni convective flow of a nanofluids (comprising two distinct kinds of carbon nanotubes ($CNT_{s}$)), in water ($H_{2}O$). Heat transportation developed by Marangoni forces happens regularly in microgravity situations, heat pipes, and in crystal growth. Therefore, Marangoni convection is considered in the flow model. A nonlinear system is constructed utilizing these assumptions which further converted to ordinary differential equations (ODEs) by accurate similarity transformations. The homotopic scheme is utilized to compute the exact solution for the proposed system. The study reveals that higher estimations of Hartmann number and Marangoni parameter speed up the fluid velocity while the opposite behavior is noted for porosity factor. Further, the rate of heat transfer shows upward trend for the Hartmann number, Marangoni parameter, nanoparticle solid volume fraction, radiation parameter whereas a downward trend is followed by the Brinkman number and porosity factor. It is fascinating to take observe that contemporary analytical outcomes validate the superb convergence with previous investigation.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79961646","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 propose a different way for solving systems of nonlinear Fredholm integral equations of the second kind. We construct our new strategy in two steps, through beginning with the linearization phase of the system of Fredholm integral equations by applying Newton method, then we pass to the discretization phase for some involved integral operator using Nystr"{o}m method. The convergence analysis of our new method is proved under some necessary conditions. At last, a numerical application to approach a nonlinear Fredholm integro-differential equation by using this new process is taken to confirm its advantage.
{"title":"Linearization-Discretization process to solve systems of nonlinear Fredholm integral equations in an infinite-dimensional context","authors":"Ilyes Sedka, S. Lemita, M. Aissaoui","doi":"10.31197/atnaa.998275","DOIUrl":"https://doi.org/10.31197/atnaa.998275","url":null,"abstract":"In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations of the second kind. We construct our new strategy in two steps, through beginning with the linearization phase of the system of Fredholm integral equations by applying Newton method, then we pass to the discretization phase for some involved integral operator using Nystr\"{o}m method. The convergence analysis of our new method is proved under some necessary conditions. At last, a numerical application to approach a nonlinear Fredholm integro-differential equation by using this new process is taken to confirm its advantage.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77340766","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 study inverse source for diffusion equation with conformable derivative: $CoD_{t}^{(gamma)}u - Delta u = Phi(t) mathcal{F}(x)$, where $0
本文研究了具有相容导数的扩散方程的逆源:$CoD_{t}^{(gamma)}u - Delta u = Phi(t) mathcal{F}(x)$，其中$0
{"title":"Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method","authors":"Ha VO THİ THANH, Ngo Hung, N. Phuong","doi":"10.31197/atnaa.1079951","DOIUrl":"https://doi.org/10.31197/atnaa.1079951","url":null,"abstract":"In this paper, we study inverse source for diffusion equation with conformable derivative: \u0000 $CoD_{t}^{(gamma)}u - Delta u = Phi(t) mathcal{F}(x)$, where $0","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76908365","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 current paper, some existence and uniqueness results for a generalized proportional Hadamard fractional integral equation are established via Picard and Picard-Krasnoselskii iteration methods together with the Banach contraction principle. A simulative example was provided to verify the applicability of the theoretical findings.
{"title":"Picard and Picard-Krasnoselskii iteration methods for generalized proportional Hadamard fractional integral equations","authors":"M. Abbas","doi":"10.31197/atnaa.1070142","DOIUrl":"https://doi.org/10.31197/atnaa.1070142","url":null,"abstract":"In the current paper, some existence and uniqueness results for a generalized proportional Hadamard fractional integral equation are established via Picard and Picard-Krasnoselskii iteration methods together with the Banach contraction principle. A simulative example was provided to verify the applicability of the theoretical findings.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91100438","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}
Many studies have been conducted using obstacle hazard values, called potential method, for connected autonomous vehicle. However, most studies were conducted for static obstacles, and those for dynamic obstacles assumed an environment without oncoming or crossing vehicles. In this study, we devise an algorithm for generating potential values considering time series characteristics using information that can be obtained through inter-vehicle communication and propose a path ?nding algorithm that uses these potential values. As an evaluation of the usefulness of the proposed method, we compare it with existing potential methods. The results show that, in some situations, the route derived by the proposed method is superior to the route derived by the existing potential method in terms of safety and timer to reach the destination.
{"title":"Proposal and Evaluation of a Dynamic Path Finding Method Using Potential Values Considering Time Series in Automatic Driving","authors":"Tomofumi Matsuzawa, Akito Fukai̇","doi":"10.31197/atnaa.1141666","DOIUrl":"https://doi.org/10.31197/atnaa.1141666","url":null,"abstract":"Many studies have been conducted using obstacle hazard values, called potential method, for connected\u0000autonomous vehicle. However, most studies were conducted for static obstacles, and those for dynamic\u0000obstacles assumed an environment without oncoming or crossing vehicles. In this study, we devise an\u0000algorithm for generating potential values considering time series characteristics using information that can\u0000be obtained through inter-vehicle communication and propose a path ?nding algorithm that uses these\u0000potential values. As an evaluation of the usefulness of the proposed method, we compare it with existing\u0000potential methods. The results show that, in some situations, the route derived by the proposed method\u0000is superior to the route derived by the existing potential method in terms of safety and timer to reach the\u0000destination.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77395185","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}
It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.
{"title":"Partially nonexpansive mappings","authors":"E. Llorens-Fuster","doi":"10.31197/atnaa.1127271","DOIUrl":"https://doi.org/10.31197/atnaa.1127271","url":null,"abstract":"It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82762534","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 authors derive several recursive and closed-form formulas for some specific values of partial Bell polynomials.
本文对部分贝尔多项式的某些特定值，给出了几个递推的和封闭的公式。
{"title":"Several recursive and closed-form formulas for some specific values of partial Bell polynomials","authors":"Wei-Shih Du, D. Lim, Feng Qi (祁锋)","doi":"10.31197/atnaa.1170948","DOIUrl":"https://doi.org/10.31197/atnaa.1170948","url":null,"abstract":"In this paper, the authors derive several recursive and closed-form formulas for some specific values of partial Bell polynomials.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72557790","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 introduce the concept of exponentially $s$-convexity in the second sense on a time scale interval. We prove among other things that if $f: [a, b]to mathbb{R}$ is an exponentially $s$-convex function, then begin{align*} &frac{1}{b-a}int_a^b f(t)Delta t &leq frac{f(a)}{e_{beta}(a, x_0) (b-a)^{2s}}(h_2(a, b))^s+frac{f(b)}{e_{beta}(b, x_0) (b-a)^{2s}}(h_2(b, a))^s, end{align*} where $beta$ is a positively regressive function. By considering special cases of our time scale, one can derive loads of interesting new inequalities. The results obtained herein are novel to best of our knowledge and they complement existing results in the literature.
{"title":"Ostrowski type inequalities via exponentially $s$-convexity on time scales","authors":"S. Georgiev, V. Darvish, E. Nwaeze","doi":"10.31197/atnaa.1021333","DOIUrl":"https://doi.org/10.31197/atnaa.1021333","url":null,"abstract":"We introduce the concept of exponentially $s$-convexity in the second sense on a time scale interval. We prove among other things that if $f: [a, b]to mathbb{R}$ is an exponentially $s$-convex function, then\u0000begin{align*}\u0000&frac{1}{b-a}int_a^b f(t)Delta t\u0000&leq frac{f(a)}{e_{beta}(a, x_0) (b-a)^{2s}}(h_2(a, b))^s+frac{f(b)}{e_{beta}(b, x_0) (b-a)^{2s}}(h_2(b, a))^s,\u0000end{align*}\u0000where $beta$ is a positively regressive function. By considering special cases of our time scale, one can derive loads of interesting new inequalities. The results obtained herein are novel to best of our knowledge and they complement existing results in the literature.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88720091","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 study the existence of solutions for a new problem of hybrid differential equations with nonlocal integro multi point boundary conditions by using the proportional fractional derivative. The presented results are obtained by using hybrid fixed point theorems for three Dhage operators. The application of theoretical conclusions is demonstrated through an example.
{"title":"A new sequential proportional fractional derivative of hybrid differential equations with nonlocal hybrid condition","authors":"Hamid Beddani, Beddani Moustafa","doi":"10.31197/atnaa.1122002","DOIUrl":"https://doi.org/10.31197/atnaa.1122002","url":null,"abstract":"In this paper, we study the existence of solutions for a new problem of hybrid differential \u0000equations with nonlocal integro multi point boundary conditions by using the proportional fractional \u0000derivative. The presented results are obtained by using hybrid fixed point theorems for three Dhage \u0000operators. The application of theoretical conclusions is demonstrated through an example.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85233522","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 integral problem for linear and nonlinear wave equations are studied.The equation involves elliptic operator L and abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data given in corresponding interpolation spaces and operators the existence, uniqueness, L^{p}-regularity properties to solutions are established. By choosing the space H and operators L, A, the regularity properties to solutions of different classes of wave equations in the field of physics are obtained.
{"title":"Regularity properties of integral problems for wave equations and applications","authors":"V. Shakhmurov, R. Shahmurov","doi":"10.31197/atnaa.1200398","DOIUrl":"https://doi.org/10.31197/atnaa.1200398","url":null,"abstract":"In this paper, the integral problem for linear and nonlinear wave equations are studied.The equation involves elliptic operator L and abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data given in corresponding interpolation spaces and operators the existence, uniqueness, L^{p}-regularity properties to solutions are established. By choosing the space H and operators L, A, the regularity properties to solutions of different classes of wave equations in the field of physics are obtained.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75340868","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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