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In this study, the necessary optimality conditions are achieved for a class of fractional optimal control problems (FOCPs) involving the Caputo–Fabrizio (CF) fractional derivative. We offer a new numerical method based on the Chebyshev cardinal functions for solving the problem. Our goal was to reduce the original problem into a nonlinear system of algebraic equations. For doing this, we approximate the state and control variables in terms of the Chebyshev cardinal functions. The operational matrices (OMs) of left and right CF fractional integrals are also derived for the Chebyshev cardinal functions. Error estimation and convergence analysis of the method are also introduced. The numerical results illustrate the effectiveness and the rapid convergence of the proposed technique. Due to the high accuracy of the solutions, the suggested method is very useful for numerical techniques in control theory.

Background:Patients need information on all aspects of prescribed drug therapy to make informed decisions about their treatment for autonomy.Purpose:This study assessed whether patients received information about potential adverse drug reactions (ADRs) from prescribed drug therapy before or after discharge following percutaneous coronary intervention (PCI). Furthermore, we sought to estimate associations with socio-demographics and concerns related to prescribed drug therapy.Methods:CONCARDPCIis a prospective multicentre cohort study including 3424 patients undergoing PCI. The study was conducted between June 2017 and May 2020 at seven large referral PCI centres in two Scandinavian countries. Clinical data were collected from patients’ medical records. Socio-demographic characteristics were obtained by self-report during index hospitalization. Four questions from the Heart Continuity of Care Questionnaire were used to determine if information about potential ADRs was provided before or after discharge. The Specific-Concerns Scale of the Beliefs about Medicines Questionnaire was used to assess concerns related to prescribed drug therapy. Logistic regression estimated whether lack of information was associated with sociodemographic characteristics.Results:Most patients were men (78%), with a mean age of 66 years (SD11, range 20-96 years) and married or living with a partner (75%). Before discharge from hospital, 59% reported being informed of potential ADRs and 50% were informed what to do if ADRs occurred. After hospital discharge, 26% reported having reviewed potential ADRs with healthcare providers, and 24% had reviewed what to do if ADRs occurred. Those who were not informed had increased concerns about their prescribed drug therapy compared to those who were informed at both time points (p<0.001). Women (51%) were less likely to receive information about potential ADRs than men (63%) (p<0.001). However, there were no substantial associations with age, education, income, or marital status.Conclusion:Four in ten patients reported not receiving information on potential ADRs from prescribed drug therapy, and this applied especially for women. Efforts to improve communication on ADRs and gender equity should be a priority.