Numerical Investigation of a Fractional Cancer Chemotherapy Effect Model Using the Homotopy Decomposition Method

Cancer, a highly aggressive neoplastic disease, has emerged as one of the leading causes of mortality worldwide. Chemotherapy remains one of the most effective therapeutic approaches for inhibiting tumor growth and reducing tumor mass. The main objective of the current work is to provide an in-depth analysis of the fractional cancer chemotherapy effect model, including qualitative and semianalytical investigation. Fixed-point theory is utilized to determine the conditions for the existence and uniqueness of solutions to the presented model. Semianalytical solutions are derived using the homotopy decomposition method (HDM) combined with the Cauchy n-integral formula. The obtained solutions are graphically simulated in MATLAB. To demonstrate the efficiency and accuracy of the HDM, the results are compared with those of the q-homotopy analysis transform method (q-HATM), revealing excellent agreement. The graphical results indicate that the chemotherapeutic drug concentration peaks at the tumor center, leading to maximum cell-killing efficacy in the central region of the tumor-affected area. Overall, this work advances theoretical and computational modeling of cancer dynamics. It delivers clinically actionable insights for designing personalized chemotherapy strategies within a fractional calculus framework.