| Summary: | In this paper, we study the averaging principle for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequality, and the H<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="normal">o</mi><mo>¨</mo></mover></semantics></math></inline-formula>lder inequality, we prove that the solution of the averaged FSDDEs converges to that of the standard FSDDEs in the sense of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula>. Our result extends some known results in the literature. Finally, an example and simulation is performed to show the effectiveness of our result.
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