{"title":"高阶分式方程及相关时变伪过程","authors":"Fabrizio Cinque, Enzo Orsingher","doi":"10.1016/j.jmaa.2024.129026","DOIUrl":null,"url":null,"abstract":"<div><div>We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129026"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Higher-order fractional equations and related time-changed pseudo-processes\",\"authors\":\"Fabrizio Cinque, Enzo Orsingher\",\"doi\":\"10.1016/j.jmaa.2024.129026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"543 2\",\"pages\":\"Article 129026\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X2400948X\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X2400948X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Higher-order fractional equations and related time-changed pseudo-processes
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.