An emerging treatment tool which uses replication-competent viruses to dissipate cancers without causing deficit to normal tissues, named as oncolytic virotherapy, is discussed in the article. We analysed a fractional delay dynamical model on the oncolytic virotherapy compositing viral lytic cycle and virus-specific cytotoxic T lymphocyte (CTL) response. We used a well known Caputo fractional derivative to analyse the structure of the given dynamical model. Using the literature of fixed-point theory, the given time-delay model is specified to have existence of a unique solution. We established different types of graphical simulations for the various values of R-0 and R-1 . We observed a different behaviour of the given fractional model as compare to the integer order model. The given algorithm is smooth in use and reliable to apply on different delay dynamical models. (C) 2021 Elsevier Ltd. All rights reserved.