  In this paper, existence and uniqueness of solutions to a non-linear, initial
value problem is studied. In particular, we consider a special type of problem
which physically represents the time evolution of particle number density
resulted due to the coagulation and fragmentation process. The coagulation
kernel is chosen from a huge class of functions, both singular and non-singular
in nature. On the other hand, fragmentation kernel includes practically
relevant non-singular unbounded functions. Moreover, both the kernels satisfy a
linear growth rate of particles at infinity. The existence theorem includes
lesser restrictions over the kernels as compared to the previous studies.
Furthermore, strong convergence results on the sequence of functions are used
to establish the existence theory.
