2024/02/21 by Fabrizio Cinque, Enzo Orsingher, Cinque, Fabrizio +1 · 2 citations
Engineering · Mathematics · #35R11 #60K99 #Advanced Control Systems Design #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2402.13691
openalex publication_date 2024/02/21 · openalex created_date 2024/02/23 · openalex updated_date 2026/07/28
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 pseudo-subordinators as well as its pseudo-inverse. 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 its inverse.