Almost automorphic mild solutions to fractional partial difference-differential equations

Lizama-Yanez, CCLizama-YanezAbadias, LucianoLucianoAbadias2025-04-232025-04-23201610.1080/00036811.2015.1064521https://sic.vriic.usach.cl/entities/publication/2232a321-cddc-4683-89b2-4ca019fb79a7We study existence and uniqueness of almost automorphic solutions for nonlinear partial difference-differential equations modeled in abstract form as (Formula presented.) for (Formula presented.) where (Formula presented.) is the generator of a (Formula presented.) -semigroup defined on a Banach space (Formula presented.) , (Formula presented.) denote fractional difference in Weyl-like sense and (Formula presented.) satisfies Lipchitz conditions of global and local type. We introduce the notion of (Formula presented.) -resolvent sequence (Formula presented.) and we prove that a mild solution of (Formula presented.) corresponds to a fixed point of (Formula presented.) We show that such mild solution is strong in case of the forcing term belongs to an appropriate weighted Lebesgue space of sequences. Application to a model of population of cells is given. © 2015 Taylor & Francis.en-US#¿NOMBRE?Almost automorphic mild solutions to fractional partial difference-differential equationshttps://doi.org/10.1080/00036811.2015.1064521