On (k,ψ)-Hilfer–Caputo Neutral Fractional Differential Equations with Multi-Point and Multi-Strip Non-Local Conditions: Existence, Uniqueness, and Ulam–Hyers Stability

We study a boundary value problem for a (k,ψ)-Hilfer–Caputo fractional neutral differential equation supplemented with multi-point and multi-strip non-local boundary conditions. An equivalent integral formulation is first derived via an auxiliary lemma. Using this representation, we establish: (i) existence and uniqueness by the Banach Contraction Principle; (ii) existence by the Krasnosel’skiĭ Fixed-Point Theorem; and (iii) existence by the Leray–Schauder Nonlinear Alternative. The results unify and extend several recent contributions in the literature on (k,ψ)-fractional calculus and neutral fractional differential equations. Three numerical examples illustrate the applicability of the theoretical findings, accompanied by solution graphs obtained via Picard iteration. Moreover, Ulam–Hyers (UH), generalized Ulam–Hyers (GUH), and Ulam–Hyers–Rassias (UHR) stability of the problem under a contraction hypothesis are investigated and illustrated through stability zone diagrams. From a symmetry perspective, we introduce the ψ-reflection x↦ψ−1(ψ(a)+ψ(b)−ψ(x)) of the non-local observation data and show that the solvability constant, existence, uniqueness and stability criteria, and Ulam–Hyers constants are invariant under it; thus, symmetric and asymmetric sensor arrangements are governed by the same criteria, whereas the solution itself is not reflection-invariant, which we quantify numerically.