Analytical and Numerical Solution to the Fractional Pendulum | Chapter 4 | Research Updates in Mathematics and Computer Science Vol. 3

 In this paper, we study the fractional pendulum oscillator equation. We solve it both numerically using finite differences method and analytically. The analytical solution is obtained by replacing the original oscillator using an integer-order oscillator. We also compare the numerical solution with the anlalytical solution obtained making use of the Chebyshev-homotopy method (KBM).

Author(s) Details:

Alvaro H. Salas,
Fizmako Research Group, Universidad Nacional de Colombia, Colombia.

Please see the link here: https://stm.bookpi.org/RUMCS-V3/article/view/13982

Approximation of the Mittag-Leffler Functions by Elementary Functions with Physics Applications | Chapter 8 | Current Perspective to Physical Science Research Vol. 7

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illustrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

Author(s) Details:

Alvaro H. Salas S.,
Universidad Nacional de Colombia, Fizmako Research Group, Bogotá, Colombia.

Please see the link here: https://stm.bookpi.org/CPPSR-V7/article/view/13471