Covid-19 is a highly infectious disease caused by novel Corona virus SARS-CoV-2, affecting the whole world. In thispaper, we introduce and apply two iterative methods, RMsDTM and R2KM, to obtain approximate values of Covid-19cases in Morocco. We also compare the approximations of both methods and see that the solution of RMsDTM ismore accurate.
{"title":"COVID-19 CASES IN MOROCCO: A COMPARATIVE ANALYSIS","authors":"Poonam Garg, Surbhi Madan, Ritu Arora, Dhiraj Singh","doi":"10.53006/rna.1015199","DOIUrl":"https://doi.org/10.53006/rna.1015199","url":null,"abstract":"Covid-19 is a highly infectious disease caused by novel Corona virus SARS-CoV-2, affecting the whole world. In thispaper, we introduce and apply two iterative methods, RMsDTM and R2KM, to obtain approximate values of Covid-19cases in Morocco. We also compare the approximations of both methods and see that the solution of RMsDTM ismore accurate.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47531274","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 work, we investigate the strong convergence of the sequences generated by the shrinking projection method and the parallel monotone hybrid method to find a common fixed point of a finite family of $mathcal{G}$-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. We also give some numerical examples and provide application to signal recovery under situation without knowing the type of noises. Moreover, numerical experiments of our algorithms which are defined by different types of blurred matrices and noises on the algorithm to show the efficiency and the implementation for LASSO problem in signal recovery.
{"title":"A modified parallel monotone hybrid algorithm for a finite family of $mathcal{G}$-nonexpansive mappings apply to a novel signal recovery","authors":"K. Kankam, P. Cholamjiak, W. Cholamjiak","doi":"10.53006/rna.1122092","DOIUrl":"https://doi.org/10.53006/rna.1122092","url":null,"abstract":"In this work, we investigate the strong convergence of the sequences generated by the shrinking projection method and the parallel monotone hybrid method to find a common fixed point of a finite family of $mathcal{G}$-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. We also give some numerical examples and provide application to signal recovery under situation without knowing the type of noises. Moreover, numerical experiments of our algorithms which are defined by different types of blurred matrices and noises on the algorithm to show the efficiency and the implementation for LASSO problem in signal recovery.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42468976","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 characterize the completeness of fuzzy quasi-metric spaces by means of a fixed point theorem of Kannan-type. Thus, we extend the classical characterization of metric completeness due to Subrahmanyam as well as recent results in the literature on the characterization of quasi-metric completeness and fuzzy metric completeness, respectively. We also introduce and discuss contractions of Chatterjea-type in this asymmetric context.
{"title":"Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces","authors":"Salvador ROMAGUERA BONİLLA","doi":"10.53006/rna.1140743","DOIUrl":"https://doi.org/10.53006/rna.1140743","url":null,"abstract":"We characterize the completeness of fuzzy quasi-metric spaces by means of a fixed point theorem of Kannan-type. Thus, we extend \u0000the classical characterization of metric completeness due to Subrahmanyam as well as recent results in the literature on the characterization of \u0000quasi-metric completeness and fuzzy metric completeness, respectively. We also introduce and discuss contractions of Chatterjea-type in this asymmetric context.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41836443","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 evolutionary operations fromdiverse fields of engineering and physical sciences go through abrupt modifications of state at specific moments of time among periods of non-stop evolution. These operations are more conveniently modeled via impulsive differential equations and inclusions. In this work, firstly we address the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions related to Caputo derivative in Banach spaces when the linear part is sectorial. Secondly, we determine the enough, conditions for the controllability of the studied control problem. We apply effectively fixed point theorems, contraction mapping, multivalued analysis and fractional calculus. Moreover, we enhance our results by introducing an illustrative examples.
{"title":"Existence and controllability of fractional evolution inclusions with impulse and sectorial operator","authors":"N. Alsarori, K. Ghadle","doi":"10.53006/rna.1018780","DOIUrl":"https://doi.org/10.53006/rna.1018780","url":null,"abstract":"Many evolutionary operations fromdiverse fields of engineering and physical sciences go through\u0000abrupt modifications of state at specific moments of time among periods of non-stop evolution.\u0000These operations are more conveniently modeled via impulsive differential equations and inclusions.\u0000In this work, firstly we address the existence of mild solutions for nonlocal fractional impulsive\u0000semilinear differential inclusions related to Caputo derivative in Banach spaces when the\u0000linear part is sectorial. Secondly, we determine the enough, conditions for the controllability of\u0000the studied control problem. We apply effectively fixed point theorems, contraction mapping,\u0000multivalued analysis and fractional calculus. Moreover, we enhance our results by introducing an\u0000illustrative examples.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47729646","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 diffusion equation with conformable derivative. The main goal is to prove the convergence of the mild solution to our problem when the order of fractional Laplacian tends to $1^-$. The principal techniques of our paper is based on some useful evaluations for exponential kernels.
{"title":"Note on the convergence of fractional conformable diffusion equation with linear source term","authors":"Tien Nguyen","doi":"10.53006/rna.1144709","DOIUrl":"https://doi.org/10.53006/rna.1144709","url":null,"abstract":"In this paper, we study the diffusion equation with conformable derivative. The main goal is to prove the convergence of the mild solution to our problem when the order of fractional Laplacian tends to $1^-$. The principal techniques of our paper is based on some useful evaluations for exponential kernels.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42513038","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}
A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.
{"title":"ON THE CONVERGENCE OF THE SIXTH ORDER HOMEIER LIKE METHOD IN BANACH SPACES","authors":"Suma P B, M. E. Shobha, S. George","doi":"10.53006/rna.1138201","DOIUrl":"https://doi.org/10.53006/rna.1138201","url":null,"abstract":"A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44220449","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}
Nowadays, a number of classical order results are being analyzed in the sense of fractional derivatives. In this research work, we discuss two different boundary value problems. In the first half of the paper, we generalize an integer-order boundary value problem into fractional-order and then we demonstrate the existence and uniqueness of the solution subject to the Caputo fractional derivative. First, we recall some results and then justify our main results with the proofs of the given theorems. We conclude our results by presenting an illustrative example. In the other half of the paper, we extend the Banach's contraction theorem to prove the existence and uniqueness of the solution to a sequential Caputo fractional-order boundary value problem.
{"title":"Some novel analysis on two different Caputo-type fractional-order boundary value problems","authors":"Zouaoui Bekri, V. S. Ertürk, Pushpendra Kumar","doi":"10.53006/rna.1114063","DOIUrl":"https://doi.org/10.53006/rna.1114063","url":null,"abstract":"Nowadays, a number of classical order results are being analyzed in \u0000the sense of fractional derivatives. In this research work, we \u0000discuss two different boundary value problems. In the first half of \u0000the paper, we generalize an integer-order boundary value problem \u0000into fractional-order and then we demonstrate the existence and \u0000uniqueness of the solution subject to the Caputo fractional \u0000derivative. First, we recall some results and then justify our main \u0000results with the proofs of the given theorems. We conclude our \u0000results by presenting an illustrative example. In the other half of \u0000the paper, we extend the Banach's contraction theorem to prove the \u0000existence and uniqueness of the solution to a sequential Caputo \u0000fractional-order boundary value problem.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71186305","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 purpose of this research is to investigate the result of Katugampola kinetic fractional equations containing the first kind of generalized Bessel's function. This paper considers the manifold generality of the first kind generalized Bessel's function in form of the solution of Katugampola kinetic fractional equations. The $tau$ Laplace transform technique is used to obtain the result. In addition, a graphical representation is included for viewing the behavior of the gained solutions.
{"title":"Katugampola kinetic fractional equation with its solution","authors":"E. Mittal, Diksha Sharma, Sunil Dutt Prohit","doi":"10.53006/rna.1061458","DOIUrl":"https://doi.org/10.53006/rna.1061458","url":null,"abstract":"The purpose of this research is to investigate the result of Katugampola kinetic fractional equations containing the first kind of generalized Bessel's function. This paper considers the manifold generality of the first kind generalized Bessel's function in form of the solution of Katugampola kinetic fractional equations. The $tau$ Laplace transform technique is used to obtain the result. In addition, a graphical representation is included for viewing the behavior of the gained solutions.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44273309","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, with aid of generating functions, the authors present several recurrence relations and identities for generalized derangement numbers involving generalized harmonic numbers and the Stirling numbers of the first kind.
本文借助生成函数，给出了广义调和数和第一类Stirling数的广义无序数的几个递推关系和恒等式。
{"title":"Several recurrence relations and identities on generalized derangement numbers","authors":"M. C. Dağlı, Feng Qi (祁锋)","doi":"10.53006/rna.1002272","DOIUrl":"https://doi.org/10.53006/rna.1002272","url":null,"abstract":"In the paper, with aid of generating functions, the authors present several recurrence relations and identities for generalized derangement numbers involving generalized harmonic numbers and the Stirling numbers of the first kind.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44998043","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":"Equivalents of various maximum principles","authors":"Sehie Park","doi":"10.53006/rna.1107320","DOIUrl":"https://doi.org/10.53006/rna.1107320","url":null,"abstract":"","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48070594","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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