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In this paper, we examine the time-dependent two-dimensional cable equation of fractional order in terms of the Caputo fractional derivative. This cable equation plays a vital role in diverse areas of electrophysiology and modeling neuronal dynamics. This paper conveys a precise semi-analytical method called the q-homotopy analysis transform method to solve the fractional cable equation. The proposed method is based on the conjunction of the q-homotopy analysis method and Laplace transform. We explained the uniqueness of the solution produced by the suggested method with the help of Banach's fixed-point theory. The results obtained through the considered method are in the form of a series solution, and they converge rapidly. The obtained outcomes were in good agreement with the exact solution and are discussed through the 3D plots and graphs that express the physical representation of the considered equation. It shows that the proposed technique used here is reliable, well-organized and effective in analyzing the considered non-homogeneous fractional differential equations arising in various branches of science and engineering. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present work is to obtain an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM). The considered nonlinear mathematical model has been effectively employed to elucidate the evolution of smoking in a population and its impact on public health in a community. We find some new approximate solutions in a series form, which converges rapidly, and the proposed algorithm provides auxiliary parameters, which are very reliable and feasible in controlling the convergence of obtained approximate solutions. Further, we present novel simulations for all cases of results to validate the applicability and effectiveness of proposed scheme. The outcomes of the study reveal that the q-HATM is computationally very effective to analyse nonlinear fractional differential equations arises in daily life problems. [ABSTRACT FROM AUTHOR]