| Summary: | In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mi>B</mi><mi>C</mi><mo>(</mo><msub><mi>R</mi><mo>+</mo></msub><mo>)</mo><mo>.</mo><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula> In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions.
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