ஜர்னல் ஆஃப் அப்ளைடு & கம்ப்யூட்டேஷனல் கணிதம்

In the history of mathematics, there are number of conjectures, unsolved till date, Collatz Conjecture is one of them. Lother Collatz introduced a conjecture in which a series of numbers get generated called hailstone numbers, a long chain of numbers, all ended to 1. This conjecture may be considered true if the sequence would not either enter a repeating cycle or increase without bound. In this paper a tangible solution is given that anticipate that no such repeated sequence is possible that increases without bound. Hence support the truthfulness of Conjecture. May be it helps the mathematicians to achieve a pragmatic mode.

This work presents a transformation of the classical thermal diffusion equation into a fractional thermal diffusion equation with respect to time, considering consistency with the dimensionality of time

This work consists in calculating values of thermal conductivity and the suitable thickness, of a thermal insulator called "thermisorel", by the coupling of the time fractional diffusion equation and the genetic algorithm, taking into account the data and the objectives of the experiment in the article [1].

This work consists in studying the adequacy of the experimental results and the theoretical results obtained from the time fractional diffusion equation on the variation of the temperature, in transient regime, during the heating of a thermal insulator. called "thermisorel".