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This study develops a fractional model using the Caputo–Fabrizio derivative with order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> for platelet-poor plasma arising in a blood coagulation system. The existence of solutions ensures that there are solutions to the considered system of equations. Approximate solutions to the recommended model are presented by selecting different numbers of fractional orders and initial conditions (ICs). For each case, graphs of solutions are supplied through different dimensions.