Ramasamy, SivaranjaniKarthikeyan, KulandhaivelSenthilprabu, ThangaveluEge, Ozgur2026-09-262026-09-2620250354-5180https://doi.org/10.2298/FIL2524607Rhttps://hdl.handle.net/11454/134373The controllability of ABC nonlinear neutral implicit integro-differential equation of fractional order 0 < 1 with delay in state and control has been examined in this work. To obtain the controllability results of the defined problem, we specifically apply the k-set contraction mapping and Darbo fixed point theorem. The provided example is used to verify the findings. The graphical illustrations are exhibited to view the orthogonal eigen-vectors corresponding to the solution.en10.2298/FIL2524607Rinfo:eu-repo/semantics/openAccessFractional DerivativeImplicit Neutral Differential EquationsControllabilitySemi-Group TheoryFixed Point TheoryControllability of nonlinear neutral implicit ABC non-integer integro-differential equations with state and control delayArticle392486078622WOS:0016296051000012-s2.0-105020816771Q2Q20009-0004-9756-69630000-0002-4138-70670000-0002-3877-27140009-0005-8136-2875