Convoluted fractional \(C\)-semigroups and fractional abstract Cauchy problems
type: Item
instance of: scholarly article
title: Convoluted fractional \(C\)-semigroups and fractional abstract Cauchy problems
zbMATH Open document ID: 1472.47032
DOI: 10.1155/2014/357821
author: Zhan-Dong Mei
author: Jinghuai Gao
author: Ji-Gen Peng
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We present the notion of convoluted fractional \(C\)-semigroup, which is the generalization of convoluted \(C\)-semigroup in the Banach space setting. We present two equivalent functional equations associated with convoluted fractional \(C\)-semigroup. Moreover, the well-posedness of the corresponding fractional abstract Cauchy problems is studied.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7022218
zbMATH Keywords: convoluted fractional \(C\)-semigroup
zbMATH Keywords: functional equations
zbMATH Keywords: well-posedness
zbMATH Keywords: fractional abstract Cauchy problem
Wikidata QID: Q59036536
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/357821
OpenAlex ID: W2066953019
cites work: Convoluted c-cosine functions and convoluted C-semigroups
cites work: Vector-valued Laplace transforms and Cauchy problems
cites work: Local integrated semigroups: Evolution with jumps of regularity
cites work: Q2716079
cites work: Integrated semigroups
cites work: Integrated semigroups and their application to complete second order Cauchy problems
cites work: Laplace Transforms and α-Times Integrated Semigroups
cites work: \(a\)-times integrated semigroups and fractional derivation
cites work: \(\alpha\)-times integrated semigroups \((\alpha\in \mathbb{R}^ +)\)
cites work: On generators of integrated \(C\)-semigroups and \(C\)-cosine functions
cites work: \(N\)-times integrated \(C\)-semigroups and the abstract Cauchy problem
cites work: On \(\alpha\)-times integrated \(C\)-semigroups and the abstract Cauchy problem
cites work: Q4315841
cites work: Q4323688
cites work: Q4843347
cites work: Q3129853
cites work: Abstract Cauchy problems: three approaches
cites work: THE HILLE–YOSIDA THEOREM FOR LOCAL CONVOLUTED SEMIGROUPS
cites work: Global convoluted semigroups
cites work: Convoluted \(C\)-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines
cites work: Cauchy problem for fractional diffusion equations
cites work: Q3408155
cites work: Fractional Cauchy problems on bounded domains
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Q4233638
cites work: Fractional evolution equations in Banach spaces
cites work: Linear integro-differential equations in Banach spaces
cites work: Regularized resolvent families
cites work: Regularized solutions for abstract Volterra equations
cites work: Q4276447
cites work: On fractional resolvent operator functions
cites work: Fractional abstract Cauchy problems
cites work: Fractional resolvents and fractional evolution equations
cites work: Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
cites work: On general fractional abstract Cauchy problem
cites work: On a functional equation associated with \((a, k)\)-regularized resolvent families
cites work: A novel characteristic of solution operator for the fractional abstract Cauchy problem
cites work: A characteristic of fractional resolvents
cites work: \((a,k)\)-regularized \(C\)-resolvent families: regularity and local properties
cites work: Mild solutions for abstract fractional differential equations
description: scientific article; zbMATH DE number 7022218