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Winter 2020 A subordination principle for subdiffusion equations with memory
Rodrigo Ponce
J. Integral Equations Applications 32(4): 479-493 (Winter 2020). DOI: 10.1216/jie.2020.32.479

Abstract

We study the existence of mild solutions to subdiffusion equations with memory

( ) t α u ( t ) = A u ( t ) + 0 t κ ( t s ) A u ( s ) d s , t 0 ,

with the initial condition u(0)=x, where 0<α<1, A is a closed linear operator defined on a Banach space X, the initial value x belongs to X and κ is a suitable kernel in Lloc1(+). First, we find a subordination formula for the solution operator of () and then we study its connection with the existence of mild solution to the first order diffusion equation with memory.

Citation

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Rodrigo Ponce. "A subordination principle for subdiffusion equations with memory." J. Integral Equations Applications 32 (4) 479 - 493, Winter 2020. https://doi.org/10.1216/jie.2020.32.479

Information

Received: 14 November 2019; Revised: 10 March 2020; Accepted: 1 April 2020; Published: Winter 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/jie.2020.32.479

Subjects:
Primary: 26A33
Secondary: 34A08, 45N05, 47D06

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 4 • Winter 2020
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