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The very high energy gamma-ray source HESS J1809-193 has been detected by theLHAASO and HAWC observatory beyond 100 TeV energy. It is an interestingcandidate for exploring the underlying mechanisms of gamma-ray production dueto the presence of supernova remnants, pulsar and molecular clouds close to it.We have considered the injection of the energetic cosmic rays from a pastexplosion, whose reminiscent may be SNR G011.0-00.0, which is located withinthe extended gamma-ray source HESS J1809-193. We explain the multi-wavelengthdata from the region of HESS J1809-193 with synchrotron, inverse Compton,bremsstrahlung emission of cosmic ray electrons and secondary gamma-rayproduction in interactions of cosmic ray protons with the cold protons in thelocal molecular clouds within a time-dependent framework including thediffusion loss of cosmic rays. The observational data has been modelled withthe secondary photons produced by the time-evolved cosmic ray spectrum,assuming the age of the explosion is 4500 years.

HESS J1809-193: Gamma-Ray Emission by Cosmic Rays from Past Explosion