The aim of this paper is to investigate the concept of regional observability, precisely regional reconstruction of the initial state, for a semilinear Caputo type time-fractional di usion system. The approaches attempted in this work are both based on xed point techniques that leads to a successful algorithm which is tested by numerical examples.
{"title":"Regional Reconstruction of Semilinear Caputo Type Time-Fractional Systems Using the Analytical Approach.","authors":"F. E. Alaoui, A. Boutoulout, Khalid Zguaid","doi":"10.31197/atnaa.799236","DOIUrl":"https://doi.org/10.31197/atnaa.799236","url":null,"abstract":"The aim of this paper is to investigate the concept of regional observability, precisely regional reconstruction of the initial state, for a semilinear Caputo type time-fractional di usion system. The approaches attempted in this work are both based on xed point techniques that leads to a successful algorithm which is tested by numerical examples.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76332385","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}
Our main purpose of this paper is to study the linear elliptic equation with nonlocal in time condition. The problem is taken in abstract Hilbert space H. In concrete form, the elliptic equation has been extensively investigated in many practical areas, such as geophysics, plasma physics, bioelectric field problems. Under some assumptions of the input data, we obtain the well-posed result for the solution. In the first part, we study the regularity of the solution. In the second part, we investigate the asymptotic behaviour when some paramteres tend to zero.
{"title":"Note on abstract elliptic equations with nonlocal boundary in time condition","authors":"Kim Van HO THİ","doi":"10.31197/atnaa.925768","DOIUrl":"https://doi.org/10.31197/atnaa.925768","url":null,"abstract":"Our main purpose of this paper is to study the linear elliptic equation with nonlocal in time condition. The problem is taken in abstract Hilbert space H. In concrete form, the elliptic equation has been extensively investigated in many practical areas, such as geophysics, plasma physics, bioelectric field problems. Under some assumptions of the input data, we obtain the well-posed result for the solution. In the first part, we study the regularity of the solution. In the second part, we investigate the asymptotic behaviour when some paramteres tend to zero.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83163878","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 initial boundary value problem for time-fractional Oldroyd-B fluid equation. Our model contains two Riemann-Liouville fractional derivatives which have many applications, for example, in viscoelastic flows. For the linear case, we obtain regularity results under some different assumptions of the initial data and the source function. For the non-linear case, we obtain the existence of a unique solution using Banach’s fixed point theorem.
{"title":"Existence of an initial value problem for time-fractional Oldroyd-B fluid equation using Banach fixed point theorem","authors":"Vo Viet Tri","doi":"10.31197/atnaa.943242","DOIUrl":"https://doi.org/10.31197/atnaa.943242","url":null,"abstract":"In this paper, we study the initial boundary value problem for time-fractional Oldroyd-B fluid equation. Our model contains two Riemann-Liouville fractional derivatives which have many applications, for example, in viscoelastic flows. For the linear case, we obtain regularity results under some different assumptions of the initial data and the source function. For the non-linear case, we obtain the existence of a unique solution using Banach’s fixed point theorem.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78464696","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 have investigated the heat transfer in a circular cylindrical pipe for Hagen-Poiseuille ow and used MATLAB as a scienti c tool to plot the graphs. The calculations for the axial heat conduction and the temperature gradient have been performed for both upstream and downstream ows. In this experiment, the results are plotted graphically for the di erent uids like Air, Water, Milk, Glycerin and Mercury. The physical trends of the plotted curves represent the values of heat transfer that were di erent in Hydrogen and Air; on the contrary rest of the uids were behaving similarly when temperature was taken as an exponential function and for sinusoidal function all the uids were behaving in a similar manner.
{"title":"Hagen-Poiseuille Flow in Circular Cylinder when Temperature is Exponential and Sinusoidal Function of Length","authors":"Radhika Khandelwal, S. Agarwal","doi":"10.31197/atnaa.954432","DOIUrl":"https://doi.org/10.31197/atnaa.954432","url":null,"abstract":"In this paper, we have investigated the heat transfer in a circular cylindrical pipe for Hagen-Poiseuille ow and used MATLAB as a scienti c tool to plot the graphs. The calculations for the axial heat conduction and the temperature gradient have been performed for both upstream and downstream ows. In this experiment, the results are plotted graphically for the di erent uids like Air, Water, Milk, Glycerin and Mercury. The physical trends of the plotted curves represent the values of heat transfer that were di erent in Hydrogen and Air; on the contrary rest of the uids were behaving similarly when temperature was taken as an exponential function and for sinusoidal function all the uids were behaving in a similar manner.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"291 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84972054","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, we introduce some new fractional integral inequalities of Minkowski’s type by using Riemann-Liouville fractional integral operator. We replace the constants that appear on Minkowski’s inequality by two positive functions. Further, we establish some new fractional inequalities related to the reverse Minkowski type inequalities via Riemann-Liouville fractional integral. Using this fractional integral operator, some special cases of reverse Minkowski type are also discussed.
{"title":"NEW GENERALIZATION OF REVERSE MINKOWSKI’S INEQUALITY FOR FRACTIONAL INTEGRAL","authors":"Tariq A. Aljaaidi, D. Pachpatte","doi":"10.31197/atnaa.756605","DOIUrl":"https://doi.org/10.31197/atnaa.756605","url":null,"abstract":"In this research, we introduce some new fractional integral inequalities of Minkowski’s type by using Riemann-Liouville fractional integral operator. We replace the constants that appear on Minkowski’s inequality by two positive functions. Further, we establish some new fractional inequalities related to the reverse Minkowski type inequalities via Riemann-Liouville fractional integral. Using this fractional integral operator, some special cases of reverse Minkowski type are also discussed.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77464247","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}
Fatima Sİ BACHİR, Abbas Said, Maamar Benbachir, M. Benchohra
This work deals with a class of Hilfer-Hadamard differential equations. Existence and stability of solutions are presented. We use an appropriate fixed point theorem.
{"title":"Hilfer-Hadamard Fractional Differential Equations; Existence and Attractivity","authors":"Fatima Sİ BACHİR, Abbas Said, Maamar Benbachir, M. Benchohra","doi":"10.31197/atnaa.848928","DOIUrl":"https://doi.org/10.31197/atnaa.848928","url":null,"abstract":"This work deals with a class of Hilfer-Hadamard differential equations. Existence and stability of solutions are presented. We use an appropriate fixed point theorem.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83376336","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}
Eman S. A. Abujarad, Mohammed H. A. AbuJarad, T. Abdeljawad, F. Jarad
In this paper, the k-integral operators for analytic functions dened in the open unit disc U = fz 2 C : jzj < 1g are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satised by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given.
{"title":"Some Properties for Certain Subclasses of Analytic Functions Associated with $k-$Integral Operators","authors":"Eman S. A. Abujarad, Mohammed H. A. AbuJarad, T. Abdeljawad, F. Jarad","doi":"10.31197/atnaa.825204","DOIUrl":"https://doi.org/10.31197/atnaa.825204","url":null,"abstract":"In this paper, the k-integral operators for analytic functions dened in the open unit disc U = fz 2 C : jzj < 1g are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satised by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"88 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73355320","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}
Multi-layer boundary value problems have received a great deal of attention in the past few years. This is due to the fact that they model many engineering applications. Examples of applications include fluid flow though multi-layer porous media such as ground water and oil reservoirs. In this work, we present a new method for solving multi-layer boundary value problems. The method is based on an efficient adaption of the classical shooting method, where a boundary value problem is solved by means of solving a sequence of initial value problems. We propose, an alternating forward-backward shooting strategy that reduces computational cost. Illustration of the method is presented on application to fluid flow through multi-layer porous media. The examples presented suggested that the method is reliable and accurate.
{"title":"Forward-Backward Alternating Parallel Shooting Method for Multi-layer Boundary Value Problems","authors":"M. Hajji","doi":"10.31197/atnaa.753561","DOIUrl":"https://doi.org/10.31197/atnaa.753561","url":null,"abstract":"Multi-layer boundary value problems have received a great deal of attention in the past few years. This is due to the fact that they model many engineering applications. Examples of applications include fluid flow though multi-layer porous media such as ground water and oil reservoirs. In this work, we present a new method for solving multi-layer boundary value problems. The method is based on an efficient adaption of the classical shooting method, where a boundary value problem is solved by means of solving a sequence of initial value problems. We propose, an alternating forward-backward shooting strategy that reduces computational cost. Illustration of the method is presented on application to fluid flow through multi-layer porous media. The examples presented suggested that the method is reliable and accurate.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90596328","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 article, we research the diabetes model and its consequences using the Caputo and Atangana Baleanu fractional derivatives. The presence and uniqueness are strongly mentored by the fixed point theorem and the approach to Picard - Lindelof. A deterministic mathematical model corresponding to the fractional derivative of diabetes mellitus. The Laplace transformation is used for the diagnostic structure of the diabetes model. Finally, numerical calculations are made to illustrate the effect of changing the fractional-order to obtain the theoretical results, and comparisons are made for the Caputo and Atangana Baleanu derivative. The results of the following work by controlling plasma glucose with the fractional-order model make it a suitable candidate for controlling human type 1 diabetes.
{"title":"Analysis and Simulation of Fractional-Order Diabetes Model","authors":"M. Farman, A. Akgül, Aqeel Ahmad","doi":"10.31197/atnaa.778506","DOIUrl":"https://doi.org/10.31197/atnaa.778506","url":null,"abstract":"In this article, we research the diabetes model and its consequences using the Caputo and Atangana Baleanu fractional derivatives. The presence and uniqueness are strongly mentored by the fixed point theorem and the approach to Picard - Lindelof. A deterministic mathematical model corresponding to the fractional derivative of diabetes mellitus. The Laplace transformation is used for the diagnostic structure of the diabetes model. Finally, numerical calculations are made to illustrate the effect of changing the fractional-order to obtain the theoretical results, and comparisons are made for the Caputo and Atangana Baleanu derivative. The results of the following work by controlling plasma glucose with the fractional-order model make it a suitable candidate for controlling human type 1 diabetes.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86758270","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}
{"title":"EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR FRACTIONAL NEUTRAL VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS","authors":"Ahmed A. Hamoud","doi":"10.31197/atnaa.799854","DOIUrl":"https://doi.org/10.31197/atnaa.799854","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85798265","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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