This paper investigates the well-posedness of a new class of fractional differential inclusions of Liouville–Caputo type, governed by a family of maximal monotone operators \(\mathbb {A}(t), t \in [0,T]\) , in an infinite-dimensional Hilbert space \(\mathbb {H}\) . The proposed model incorporates two single-valued perturbations, including an integral term of Volterra type. Assuming a Hölder variation of the operator family with respect to the Vladimirov pseudo-distance, we establish our main result via a full discretization scheme. This approach relies on a suitable subdivision of the time interval [0, T], together with key properties of Yosida approximations, resolvent mappings, and an enhanced fractional Grönwall’s inequality. Finally, to demonstrate the applicability of our theoretical result, we provide an application to non-regular electrical circuits involving fractional-order capacitors, and present numerical simulations that further support and illustrate our findings.
