Solution of QCD$\otimes$QED coupled DGLAP equations at NLO

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In this work, we present an analytical solution for QCD$\otimes$QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in perturbative QCD using double Laplace transform.

• This technique is applied to obtain the singlet, gluon and photon distribution functions and also the proton structure function.
• We also obtain contribution of photon in proton at LO and NLO at high energy and successfully compare the proton structure function with HERA data \cite{12} and APFEL results \cite{7}.
• Some comparisons also have been done for the singlet and gluon distribution functions with the MSTW results\cite{9}.