New solutions of time-fractional cancer tumor models using modified He-Laplace algorithm.

Cancer develops through cells when mutations build up in different genes that control cell proliferation. To treat these abnormal cells and minimize their growth, various cancer tumor samples have been modeled and analyzed in literature. The current study is focused on the investigation of more generalized cancer tumor model in fractional environment, where net killing rate is taken into account in different domains. Three types of killing rates are considered in the current study including time and position dependent killing rates, and concentration of cells based killing rate. A hybrid mechanism is proposed in which different homotopies are used with perturbation technique and Laplace transform. This leads to a convenient algorithm to tackle all types of fractional derivatives efficiently. The convergence and error bounds of the proposed scheme are computed theoretically by proving related theorems. In the next phase, convergence and validity is analyzed numerically by calculating residual errors round the fractional domain. It is observed that computed errors are very less in the entire fractional domain. Moreover, comparative analysis of Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional derivatives is also performed graphically to discern the effect of different fractional approaches on the solution profile. Analysis asserts the reliability of proposed methodology in the matter of intricate fractional tumor models, and hence can be used to other complex physical phenomena.