University of Tabriz Computational Methods for Differential Equations 2345-3982 9 3 2021 07 01 Stability and bifurcation of fractional tumor-immune model with time delay 692 709 10334 10.22034/cmde.2020.37915.1672 EN Javad Alidousti Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran. Elham Ghafari Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran. Journal Article 2020 01 15 ‎The present study aims are to analyze a delay tumor-immune fractional-order system to describe the rivalry among the immune system and tumor cells. Given that the dynamics of this system depend on the time delay parameter, we examine the impact of time delay on this system to attain better compatibility with actuality. For this purpose, we analytically evaluated the stability of the system’s equilibrium points. It is shown that Hopf bifurcation occurs in the fractional system when the delay parameter passes a certain value. Finally, by using numerical simulations, the analytical results were compared to the numerical results to acquire several dynamical behaviors of this system. Fractional differential equations time delay Stability analysis Hopf Bifurcation https://cmde.tabrizu.ac.ir/article_10334_9ab6cb7a552dab94cf95c3adb92a2caa.pdf