arXiv subjects

Eduardo Santillan Marcus

Publications and source records attributed to Eduardo Santillan Marcus.

3 recordsLinked to original sources

arXiv2019

Approximate solutions of one dimensional systems with fractional derivative

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution of ordinary fractional differential equations. Due to the non-locality of the fractional derivative, we may establish an equivalence between fractional oscillators and ordinary oscillators with a dissipative term.

math.NA↗

arXiv2015

On the Initial-Boundary Problem for the Time-Fractional Diffusion Equation in the Quarter Plane

Taking into account the asymptotic behavior of some Wright functions and the existence of bounds for the Mainardi and the Wright function $W(-x,\fracα{2}, 1)$ in $\mathbb{R}^+$ , three different initial-boundary-value problems for the time-fractional diffusion equation in the quarter plane, where the time-fractional derivative is taken in the Caputo sense of order $α$ $\in (0,1)$ are solved. Moreover, the limit when $α\nearrow 1$ of the respective solutions are analyzed, recovering the respective solutions of the classical boundary-value problems when $α=1$ and the fractional diffusion equation becomes the heat equation.

math.AP↗

arXiv2014

A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation

A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ α\in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first one with a constant condition on $ x = 0 $ and the second with a flux condition)is proved and the convergence to the classical solutions is analyzed when $ α\nearrow 1$ recovering the heat equation with its respective Stefan condition.

math.AP↗