arXiv subjects

Juan J. Trujillo

Publications and source records attributed to Juan J. Trujillo.

3 recordsLinked to original sources

arXiv2015

Fractional Power-Law Spatial Dispersion in Electrodynamics

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb's law and Debye's screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type.

physics.class-ph↗

arXiv2009

A Fite type result for sequential fractional differential equations

Given the solution $f$ of the sequential fractional differential equation $_{a}D_{t}^α(_{a}D_{t}^αf)+P(t)f=0$, $t\in[b,c]$, where $-\infty<a<b<c<+\infty$, $α\in({1/2},1)$ and $P:[a,+\infty)\to[0,P_{\infty}]$, $P_{\infty}<+\infty$, is continuous, assume that there exist $t_1,t_2\in[b,c]$ such that $f(t_1)=(_{a}D_{t}^αf)(t_2)=0$. Then, we establish here a positive lower bound for $c-a$ which depends solely on $α,P_{\infty}$. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.

math.DS↗

arXiv2007

On exact solutions of a class of fractional Euler-Lagrange equations

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian $L(x(t)$, where $_a^cD_t^αx(t))$ and $0<α< 1$, such that the following is the corresponding Euler-Lagrange % \begin{equation}_tD_b^α(_a^cD_t^α) x(t)+ b(t,x(t))(_a^cD_t^αx(t))+f(t,x(t))=0. \end{equation} % At last, exact solutions for some Euler-Lagrange equations are presented. In particular, we consider the following equations % \begin{equation}_tD_b^α(_a^cD_t^αx(t))=λx(t), (λ\in R) \end{equation} % \begin{equation}_tD_b^α(_a^cD_t^αx(t))+g(t)_a^cD_t^αx(t)=f(t), \end{equation} where g(t) and f(t) are suitable functions.

math-ph↗