RT journal article
T1 Existence and uniqueness of solutions for a class of discrete-time fractional equations of order 2 < α ≤ 3
A1 Leal, C.
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Fractional Rieman-Liouville
K1 resolvent families
K1 maximal regularity
K1 equation with memory
K1 R-boundedness
AB In this paper we consider a class of linear difference equations of fractional order $2 <\alpha< 3$in the sense of Riemann–Liouville. The explicit solution for this model is provided in termsof a fractional resolvent sequence which allows to write the solution to this equation as avariation of constant formula. We also characterize the existence and uniqueness of solutionsin $l_p(N0;X)$ spaces with X being a UMD-space in terms of the R-boundedness of the operatorsymbol of the model. Moreover, we are able to relax this condition in the case of Hilbert spaces.Finally, we illustrate our results with an example that involves the generator of a contractionsemigroup.
PB Springer
SN 1432-0606
YR 2022
FD 2022
LK http://hdl.handle.net/10498/35334
UL http://hdl.handle.net/10498/35334
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026