Convolution semigroups and resolvent families of measures on hypergroups

1985 ◽  
Vol 188 (4) ◽  
pp. 449-474 ◽  
Author(s):  
Walter R. Bloom ◽  
Herbert Heyer
Keyword(s):  
Convolution Semigroups ◽  
Resolvent Families

scholarly journals Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Rodrigo Ponce
Keyword(s):  
Banach Spaces ◽  
Fractional Derivatives ◽  
Mild Solutions ◽  
Cauchy Problems ◽  
Families Of Operators ◽  
Resolvent Families

We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases0<α<1and1<α<2.

scholarly journals A Subordination Principle on Wright Functions and Regularized Resolvent Families

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Luciano Abadias ◽  
Pedro J. Miana
Keyword(s):  
Fractional Calculus ◽  
Lévy Processes ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Cauchy Problems ◽  
Convolution Properties ◽  
Vector Valued ◽  
Resolvent Families

We obtain a vector-valued subordination principle forgα,gβ-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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