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In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Caputo hybrid fractional derivatives of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>υ</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula> subjected to Dirichlet boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of the Leray–Schauder alternative theorem and Banach’s contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam–Hyers. Finally, we provide one example in order to show the validity of our results.