“…In either case, if one concentrate upon integer order operations only, then that leads to classical pantograph integro-differential [23,29] and integro-difference [6,37] equations, respectively. For the above cases the theoretical investigation related to existence and uniqueness of solution have been carried out by J. M. Cushing [14], A. Aghajani et al [2], K. Balachandran et al [7], Sarkar et al [31], Saha et al [30], Gupta et al [19], S. Etemad et al [8], B. Ahmad et al [3] and many other researchers. However, all the previously published works are primarily focused on separate cases only.…”