A subordination principle on Wright functions and regularized resolvent families

2014/12/23 by Luciano Abadias, Abadias, Luciano, Pedro J. Miana +1 · 1 citation
Mathematics · #33E12 #35R11 #47D06 #47D99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primarly #Secondary #math.CA #math.FA #msc:33E12 #msc:35R11 #msc:47D06 #msc:47D99

paper · pdf · doi:10.48550/arxiv.1412.7308

arxiv created 2014/12/23 · arxiv updated 2014/12/24

Abstract

We obtain a vector-valued subordination principle for (g_α, g_α)-regularized resolvent families which unified and improves various previous results in the literature. As a consequence we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results.

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