Existence and uniqueness of solutions for coagulation-fragmentation problems with singularity

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.