Mohamed Chohri, S. Bouriah, Salim Abdelkrim, M. Benchohra
In this article, we employ Mawhin's theory of degree of coincidence to provide an existence result for a class of problems involving non-linear implicit fractional differential equations with the exponentially fractional derivative of Caputo. Two examples are provided to demonstrate the applicability of our results.
{"title":"On Nonlinear Periodic Problems with Caputo's Exponential Fractional Derivative","authors":"Mohamed Chohri, S. Bouriah, Salim Abdelkrim, M. Benchohra","doi":"10.31197/atnaa.1130743","DOIUrl":"https://doi.org/10.31197/atnaa.1130743","url":null,"abstract":"In this article, we employ Mawhin's theory of degree of coincidence to provide an existence result for a class of problems involving non-linear implicit fractional differential equations with the exponentially fractional derivative of Caputo. Two examples are provided to demonstrate the applicability of our results.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82139982","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 initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.
{"title":"New classes of control functions for nonlinear contractions and applications","authors":"M. Berzig","doi":"10.31197/atnaa.1134524","DOIUrl":"https://doi.org/10.31197/atnaa.1134524","url":null,"abstract":"We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80382394","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}
Sachin K. Magar, Ahmed A. Hamoud, Amol D. Khandagale, K. Ghadle
In this manuscript, athours interested on the generalized Shehu transform of $Psi$-Riemann-Liouville, $Psi$-Caputo, $Psi$-Hilfer fractional derivatives. Moreover, $Psi$-Prabhakar, $Psi$-Hilfer-Prabhakar fractional derivatives and its regularized version presented in terms of the $Psi$-Mittag-Leffler type function. They are also utilised to solve several Cauchy type problems involving $Psi$-Hilfer-Prabhakar fractional derivatives and their regularised form, such as the space-time fractional advection-dispersion equation and the generalized fractional free-electron laser (FEL) equation.
{"title":"Generalized Shehu Transform to $Psi$-Hilfer-Prabhakar Fractional Derivative and its Regularized Version","authors":"Sachin K. Magar, Ahmed A. Hamoud, Amol D. Khandagale, K. Ghadle","doi":"10.31197/atnaa.1032207","DOIUrl":"https://doi.org/10.31197/atnaa.1032207","url":null,"abstract":"In this manuscript, athours interested on the generalized Shehu transform of $Psi$-Riemann-Liouville, $Psi$-Caputo, $Psi$-Hilfer fractional derivatives. Moreover, $Psi$-Prabhakar, $Psi$-Hilfer-Prabhakar fractional derivatives and its regularized version presented in terms of the $Psi$-Mittag-Leffler type function. They are also utilised to solve several Cauchy type problems involving $Psi$-Hilfer-Prabhakar fractional derivatives and their regularised form, such as the space-time fractional advection-dispersion equation and the generalized fractional free-electron laser (FEL) equation.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82071360","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. Kamrujjaman, Sadia Akter Lima, Md. Shafiqul Islam, Hazrat Ali
{"title":"Galerkin Finite Element Approach to Solve System of Nonlinear Second-Order Boundary Value Problems","authors":"M. Kamrujjaman, Sadia Akter Lima, Md. Shafiqul Islam, Hazrat Ali","doi":"10.31197/atnaa.858609","DOIUrl":"https://doi.org/10.31197/atnaa.858609","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84769256","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":"Some Neutrosophic Continuous Distributions With Applications to Neutrosophic Random Variables","authors":"Carlos Granados, A. Das, Birojit Das","doi":"10.31197/atnaa.1056480","DOIUrl":"https://doi.org/10.31197/atnaa.1056480","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"178 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77538632","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":"Multiple Nonnegative Solutions for a Class of Fourth-Order BVPs Via a New Topological Approach","authors":"Salim Benslimane, S. Georgiev, K. Mebarki","doi":"10.31197/atnaa.977625","DOIUrl":"https://doi.org/10.31197/atnaa.977625","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80800781","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":"On the integration of first order nonlinear differential equations and the conditions of Fuchs' theorem","authors":"A. Kessi, Moussa Yahi̇, T. Laadj","doi":"10.31197/atnaa.1059343","DOIUrl":"https://doi.org/10.31197/atnaa.1059343","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86783934","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":"Properties of Certain Volterra type ABC Fractional Integral Equations","authors":"D. Pachpatte, J. Nieto","doi":"10.31197/atnaa.1061019","DOIUrl":"https://doi.org/10.31197/atnaa.1061019","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"431 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77508510","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":"Neumann and Mix Boundary Value Problems on the Upper Half Plane","authors":"A. Chaudhary","doi":"10.31197/atnaa.950920","DOIUrl":"https://doi.org/10.31197/atnaa.950920","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88455543","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":"LOWER SEMI-CONTINUITY IN A GENERALIZED METRIC SPACE","authors":"M. Asadi, Alireza Khalesi̇","doi":"10.31197/atnaa.1013690","DOIUrl":"https://doi.org/10.31197/atnaa.1013690","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"245 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82761455","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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