Reliable methods to look for analytical and numerical solutions of a nonlinear differential equation arising in heat transfer with the conformable derivative

The main purpose of this paper is to conduct a complete study on analytical and numerical solutions of a nonlinear differential equation arising in heat transfer with the conformable derivative. To this end, the governing model, which is about the cooling of a lumped system with a variable specific heat, is considered, and its analytical and numerical solutions are obtained through adopting a group of well-designed techniques such as the homotopy analysis method, the operational collocation method based on Jacobi polynomials, and the finite difference method. To show the effectiveness of the schemes, comparisons are given in two-dimensional postures demonstrating an agreement between analytical and numerical solutions. In the end, the effect of the parameter alpha on the dynamical features of the obtained solutions is investigated graphically.