Background: The distribution of drugs could not be controlled in the conventional drug delivery system. This has led to the development of a smart nanoparticle-based drug delivery system, known as smart drug delivery systems. In cancer research, novel biocompatible nanocarriers have received much attention for various ranges of anticancer drugs.In the current study, the effect of a novel co-polymer "dimethyl acrylamide-trimethyl chitosan" was investigated on drug delivery of doxorubicin and paclitaxel utilizing modified fullerene nanocarrier. This study was performed via molecular dynamics simulation based on acidic pH sensitivity of the cancer microenvironment. Furthermore, hydrogen bonds, diffusion coefficient, gyration radius, and drug-carrier interaction energies were investigated here. Interestingly, a simultaneous pH and temperature-sensitive system was proposed for paclitaxel and doxorubicin for a co-polymer. A pH-sensitive and temperature-sensitive copolymer was used based on trimethyl chitosan and dimethyl acrylamide, respectively. In such a dualistic approach, co-polymer makes an excellent option to have two properties in one bio-polymer. Results: The results suggest the dramatic and indisputable role of the co-polymer in the release of doxorubicin and paclitaxel in cancerous tissues, as well as an increased biocompatibility and drug uptake in a neutral state. The validation test was performed by repeated simulations of a similar article. The results are very close to those of the reference paper .Conclusions: Overall, conjugated fullerene and dimethyl acrylamide-trimethyl chitosan (DMAA-TMC) as carriers can be a good proposition for loading, delivery, and release of anti-cancer drugs based on a pH/temperature-sensitive smart drug delivery system.