Existence and stability analysis for Caputo generalized hybrid Langevin differential systems involving three-point boundary conditions

Abstract This research inscription gets to grips with two novel varieties of boundary value problems. One them is a hybrid Langevin fractional differential equation, whilst the other coupled system equation encapsuling collective derivative known as ψ -Caputo operator. Such operators are generated by iterating local integral function respect another increasing positive Ψ. The existence solutions aforehand equations tackled using Dhage fixed point theorem, whereas their uniqueness handled Banach theorem. On top this, stability within scope Ulam–Hyers these systems also considered. Two pertinent examples presented corroborate reported results.