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Journal of Function Spaces
Volume 2015, Article ID 158145, 9 pages
http://dx.doi.org/10.1155/2015/158145
Research Article

A Subordination Principle on Wright Functions and Regularized Resolvent Families

Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received 11 December 2014; Accepted 20 February 2015

Academic Editor: Gestur Ólafsson

Copyright © 2015 Luciano Abadias and Pedro J. Miana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain a vector-valued subordination principle for -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.