Abstract
In this manuscript, we investigate the existence and the semi‐analytical solutions of the fractional‐order vector‐born disease model using the Caputo–Fabrizio fractional derivative. In this study, we have developed existence results about the solution for the problem under consideration using the results of fixed‐point theory. On the other hand, the semi‐analytical results were obtained via Laplace Adomain decomposition method. The results established using the proposed techniques are in the form of an infinite series which converges rapidly to the exact solution. Furthermore, the obtained results are compared with the result of integer‐order derivatives. The dynamics of the solution is interpreted graphically.