Zeb, A.Kumar, P.Djilali, S.Erturk, V.S.Govindaraj, V.2025-03-152025-03-15202502349-510310.1007/s40819-025-01857-22-s2.0-85218706209https://doi.org/10.1007/s40819-025-01857-2https://hdl.handle.net/20.500.14517/7749In this research article, we investigate a COVID-19 model of fractional-order defined in terms of functional shape with square root susceptible-infected interaction. Firstly, we simulate the positivity and boundedness of the solution and then calculate the nature of equilibria. For exploring the dynamics of investigated fractional-order model, we use the Hurwitz criterion and then a graph theoretical method for the derivation of a Lyapunov function. For the given model, a unique solution exists under the results of the fixed-point theory. We use the Harr wavelets method to derive the numerical solution of the investigated model. As a result, some graphical illustrations are used to ensure the theoretical results, which indicates the good agreement between numerical illustrations and theoretical findings. The motivation of this article is to show how the given square root susceptible-infected interaction model effectively explores the outbreaks of COVID-19 at various fractional-order values. The inclusion of the Caputo fractional derivative incorporates the memory effects in the proposed model. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.eninfo:eu-repo/semantics/closedAccessCovid-19 EpidemicFractional Differential EquationsHaar Wavelets MethodStability AnalysisArticleN/AQ2112