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• A reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response is presented. • Threshold parameters and equilibria are determined. • Stability analysis are rigorously established. • Numerical simulations are given to illustrate the analytical results. Despite many years of research, cancer continues to be a major worldwide concern. Several researchers proposed their mathematical models to understand and describe the dynamics of tumor cells under some cancer treatments. In this paper, we present a fractional partial differential equation system to describe the dynamics in space and time of the concentration of normal cells, tumor cells, nutrient, M1 virus, and cytotoxic T lymphocytes (CTL) cells, as well as the interaction between them. We study and analyze the equilibrium points of the presented system. The global stability of these equilibrium points is proved by constructing adequate Lyapunov functional for each equilibrium point. Furthermore, we give some numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]