OICC Press Mathematical Sciences 2251-7456 17 4 (December 2023) 2022 03 02 Solvability of some fractional differential equations in the Hölder space Hγ(R+) and their numerical treatment via measures of noncompactness 10.1007/s40096-022-00458-0 EN Hojjatollah Amiri Kayvanloo Department of Mathematics, Islamic Azad University, Mashhad, IR Mohammad Mursaleen Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, TW Aligarh Muslim University, Aligarh, 202002, IN Mohammad Mehrabinezhad Department of Mathematics, Islamic Azad University, Mashhad, IR Farzaneh Pouladi Najafabadi Department of Mathematics, Islamic Azad University, Mashhad, IR Journal Article 2022 03 02 Abstract We study the following fractional boundary value problem: Dαυ(t)+f(t,υ(t))=0,α∈(1,2],0   The goal of this paper is to bring forward a new family of measures of noncompactness and prove a fixed point theorem of Darbo type in the Hölder space . Moreover, we provide an example which supports our main result and in carrying out an proximate solution for the mentioned example with high precision we apply several numerical methods.