RT journal article
T1 Fundamental Solutions for Abstract Fractional Evolution Equations with Generalized Convolution Operators
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
AB We investigate a class of abstract fractional evolution equations governed by convolution-type derivatives associated with Sonine kernels. These generalized derivatives encompass several known fractional operators, including the Caputo--Dzhrbashyan and distributed-order derivatives. We analyze the Cauchy problem\[\partial_t(k \ast (u - u_0))(t) = -A^\alpha u(t),\]where \( k \) is a Sonine kernel, \( A \) is a closed linear operator generating a bounded analytic semigroup, and \( \alpha \in (0,1) \). Using functional analytic techniques and subordination theory, we establish well-posedness in the space of infinitely smooth vectors and derive explicit representations for the solution via Laplace transforms and fractional semigroup theory. Several examples involving the Laplacian on different function spaces are discussed to illustrate the theory.
PB Elsevier
SN 0893-9659
YR 2026
FD 2026
LK http://hdl.handle.net/10498/37335
UL http://hdl.handle.net/10498/37335
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026