The Dirichlet problem with tempered fractional derivatives

Torres Ledesma C.E.; Nyamoradi N.; Bonilla M.M.; Rodríguez J.A. · Rendiconti del Circolo Matematico di Palermo (2025) · DOI: 10.1007/s12215-025-01190-z

Resumen

This paper is devoted to the following boundary value problem with tempered fractional derivatives (Formula presented.) where α∈(0,12), σ>0, Db-α,σu,CDa+α,σu are the right Riemann-Liouville and left Caputo tempered fractional derivative respectively and f:[a,b]×R→R is a suitable Carathéodory function. In order to obtain at least one weak solution, we use minimal principle and Morse theory. To assure the (PS) conditions, a new compact embedding is presented. This work complements the previous works (Cuti Gutierrez et al. in J Appl Anal Comput 14:3496-3519, 2024; Torres Ledesma in Progr Fract Differ Appl 10:677-694, 2024, J Pseudo-Differ Oper Appl 14:62, 2023) considering the case α∈(0,12). © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2025.

Instituciones: Universidad Nacional de Trujillo