Generation theorems for fractional resolvent families

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Yun-Yi Mu ◽  
Miao Li
Keyword(s):  
Fractional Resolvent Families ◽  
Resolvent Families

A novel algebraic characteristic of fractional resolvent families

2018 ◽  
Vol 99 (2) ◽  
pp. 293-302
Author(s):  
Jie Mei ◽  
Chuang Chen ◽  
Miao Li
Keyword(s):  
Fractional Resolvent Families ◽  
Resolvent Families

scholarly journals On boundary values of fractional resolvent families

2011 ◽  
Vol 384 (2) ◽  
pp. 453-467 ◽  
Author(s):  
Chuang Chen ◽  
Miao Li ◽  
Fu-Bo Li
Keyword(s):  
Boundary Values ◽  
Fractional Resolvent Families ◽  
Resolvent Families

scholarly journals Resolvent Positive Operators and Positive Fractional Resolvent Families

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Nan-Ding Li ◽  
Ru Liu ◽  
Miao Li
Keyword(s):  
Banach Space ◽  
Fractional Differential Equations ◽  
Ordered Banach Space ◽  
Resolvent Family ◽  
Completely Monotonic ◽  
Densely Defined Operator ◽  
Fractional Resolvent Families ◽  
Fractional Differential ◽  
Densely Defined ◽  
Resolvent Families

This paper is concerned with positive α -times resolvent families on an ordered Banach space E (with normal and generating cone), where 0 < α ≤ 2 . We show that a closed and densely defined operator A on E generates a positive exponentially bounded α -times resolvent family for some 0 < α < 1 if and only if, for some ω ∈ ℝ , when λ > ω , λ ∈ ρ A , R λ , A ≥ 0 and sup λ R λ , A : λ ≥ ω < ∞ . Moreover, we obtain that when 0 < α < 1 , a positive exponentially bounded α -times resolvent family is always analytic. While A generates a positive α -times resolvent family for some 1 < α ≤ 2 if and only if the operator λ α − 1 λ α − A − 1 is completely monotonic. By using such characterizations of positivity, we investigate the positivity-preserving of positive fractional resolvent family under positive perturbations. Some examples of positive solutions to fractional differential equations are presented to illustrate our results.

scholarly journals Abstract degenerate fractional differential inclusions in Banach spaces

2017 ◽  
Vol 11 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Linear Operators ◽  
Cauchy Problems ◽  
Fractional Differential Inclusions ◽  
Caputo Derivatives ◽  
Fractional Resolvent Families ◽  
Fractional Differential ◽  
Resolvent Families ◽  
Linear Degenerate

In the paper under review, we investigate a class of abstract degenerate fractional differential inclusions with Caputo derivatives. We consider subordinated fractional resolvent families generated by multivalued linear operators, which do have removable singularities at the origin. Semi-linear degenerate fractional Cauchy problems are also considered in this context.

scholarly journals On fractional powers of generators of fractional resolvent families

2010 ◽  
Vol 259 (10) ◽  
pp. 2702-2726 ◽  
Author(s):  
Miao Li ◽  
Chuang Chen ◽  
Fu-Bo Li
Keyword(s):  
Fractional Powers ◽  
Fractional Resolvent Families ◽  
Resolvent Families

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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