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In this study, we employ the Laplace Variational Iterational Method (LVIM) as a sophisticated mathematical tool to investigate into the complex dynamics of cancer cells under the influence of chemotherapy. The LVIM, a method combining Laplace transformations and variational iteration techniques, is specifically adapted to address a system of time fractional differential equations (FDEs) that characterizes the temporal behavior of cancer cells. To enhance the efficacy of our approach, we introduce a semi-analytic version of LVIM, which proves to be a powerful and versatile tool for solving mathematical problems involving fractional derivatives. The focus of our analysis centers on elucidating the impact of chemotherapy, with a particular emphasis on drug diffusion within cancer cells and the fractality of DNA walks. Through numerical exploration encompassing varying fractional order derivatives, our study exposes nonlinear behaviors that remain secret in systems featuring only integer order derivatives. Notably, the methodology we propose is not only applicable to the specific cases examined in this research but also exhibits broad versatility, making it suitable for exploring the effects of different drugs and types of cancers. This research contributes valuable insights into the dynamics of cancer cells, aiding in the understanding of the implications for therapeutic strategies in the context of cancer treatment.

We investigate a generalization of the equation curlw→=g→ to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of Rn using classical operators from Clifford analysis. In the physically significant case n=3, two explicit solutions to the div-curl system in exterior domains of R3 are obtained following different constructions of hyper-conjugate harmonic pairs. One of the constructions hinges on the use of a radial integral operator introduced recently in the literature. An exterior Neumann boundary-value problem is considered for the div-curl system. That system is conveniently reduced to a Neumann boundary-value problem for the Laplace equation in exterior domains. Some results on its uniqueness and regularity are derived. Finally, some applications to the construction of solutions of the inhomogeneous Lamé–Navier equation in bounded and unbounded domains are discussed.