Time-lag in hadronic channel: to explore delayed VHE-flare of 3C 279

On 28 January 2018, the High Energy Stereoscopic System (H.E.S.S.) reported a significant very-high-energy (VHE) gamma-ray activity, occurring nearly 11 days after the high-energy (HE) gamma-ray flare observed by \textit{Fermi}-LAT from the blazar 3C 279. It has long been considered a candidate site for accelerating particles to ultra-high energies (UHE) and producing subsequent secondaries. Such an event can be crucial to explore the different phenomena of secondary production from the UHEs and viable to understand the energetics of the sources. Our study finds that the multi-wavelength flare, spanning UV, optical, X-rays, and HE gamma rays, originates from leptonic emissions, whereas the delayed VHE activity by proton synchrotron emission within the source, results from the extended duration of particle acceleration. To explain the prolonged electromagnetic emission, our model requires a magnetic field luminosity (L$'_B$) $6.1 \times 10^{43}$ erg/sec, a proton luminosity (L$'_{p}$) $1.2\times 10^{46}$ erg/sec in the jet frame.