ABSTRACT In this paper, we study a boundary value problem for a hybrid variable‐order Caputo–Hadamard fractional sequential integro‐differential equation with nonseparated boundary conditions. The problem involves variable‐order fractional derivatives together with nonlinear integral operators. We reformulate the problem as a fixed point problem in the Banach space of continuous functions. By using the measure of noncompactness and Darbo's fixed point theorem, we prove the existence of solutions. Additional conditions are imposed to obtain uniqueness and Ulam–Hyers–Rassias stability. To support the obtained results, we provide illustrative examples and graphical results. These examples show that the assumptions depend on the choice of the interval , which in turn affects the admissible region.
Verma et al. (Thu,) studied this question.