2010/11/05 by Mirko D’Ovidio, Mirko D'Ovidio, D'Ovidio, Mirko
Mathematics · #60E05 #60G52 #Analytic and geometric function theory #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Probability (math.PR) #math.PR #msc:60E05 #msc:60G52
paper · pdf · doi:10.48550/arxiv.1011.1424
Accepted by Stochastic Processess and Their Applications
openalex publication_date 2010/11/05 · arxiv created 2012/06/04 · arxiv updated 2012/06/05 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the explicit laws of certain stable processes turn out to be fundamental. This paper directs one's efforts towards the explicit representation of solutions to fractional and anomalous diffusions related to Sturm-Liouville problems of fractional order associated to fractional power function spaces. Furthermore, we study a new version of the Bochner's subordination rule and we establish some connections between subordination and space-fractional operator