The very-high-energy γ-ray source HESS J1809-193 has been detected by the LHAASO and HAWC observatory beyond 100 TeV energy. It is an interesting candidate for exploring the underlying mechanisms of γ-ray production due to the presence of supernova remnants, pulsars, and molecular clouds close to it. We have considered the injection of the energetic cosmic rays from a past explosion, whose reminiscent may be SNR G011.0-00.0, which is located within the extended γ-ray source HESS J1809-193. We explain the multiwavelength data from the region of HESS J1809-193 with synchrotron, inverse Compton, and bremsstrahlung emission of cosmic-ray electrons and secondary γ-ray production in interactions of cosmic-ray protons with the cold protons in the local molecular clouds within a time-dependent framework including the diffusion loss of cosmic rays. The observational data have been modeled with the secondary photons produced by the time-evolved cosmic-ray spectrum assuming the age of the explosion is 4500 yr.