Modanli, MahmutAkgül, Ali2024-12-242024-12-2420212576-5299https://doi.org10.1080/25765299.2021.1958490https://hdl.handle.net/20.500.12604/4053In this paper, the linear and nonlinear fractional order time varying linear dynamical systems model has been studied. The homotopy perturbation method is used to find the approximation solution. The obtained approximation solution is effective which is close to the exact solution. The results showed that the method is effective and useful. This method produce better approximations than the ones produced with the standard weighted residual methods. Additionally, some useful reproducing kernel functions have been obtained. Solutions of the models can be obtained by the reproducing kernel method with these reproducing kernel functions. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.eninfo:eu-repo/semantics/openAccessApproximate solutionsbounded linear operatornumerical methodreproducing kernel functionsArticle281300308Q12-s2.0-8511160026910.1080/25765299.2021.1958490