In this paper, we study a class of second-order fractional boundary value problems involving Θ-Caputo derivatives of different orders. By reformulating the problem to an integral equation, we introduce an appropriate notion of a mild solution in the Θ-fractional framework. Existence results are obtained via Krasnoselskii’s fixed point theorem, while uniqueness is established using the Banach contraction principle under suitable Lipschitztype conditions. The obtained results extend several earlier works on Caputo, Hadamard– Caputo, and Riemann–Liouville fractional derivatives. Two examples are presented to illustrate the applicability of the theoretical results.
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