Existence of solution for fractional Langevin equation: Variational approach

doi:https://doi.org/10.14232/ejqtde.2014.1.54

Open AccessArticle10.14232/ejqtde.2014.1.54

Existence of solution for fractional Langevin equation: Variational approach

César E. Torres Ledesma-2014-01-01-Electronic journal of qualitative theory of differential equations

36

TL;DRAbstract

We consider the Dirichlet problem for the fractional Langevin equation with two fractional order derivatives \begin{align*} -{_{0}}D_{t}^{\alpha}(_{0}D_{t}^{\alpha}u(t)) &= f(t,u(t), {_{0}}D_{t}^{\alpha}u(t)), \quad t\in [0,1],\\ u(0) &= u(1) = 0. \end{align*} The existence of a nontrivial solution is stated through an iterative method based on mountain pass techniques.

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We consider the Dirichlet problem for the fractional Langevin equation with two fractional order derivatives \begin{align*} -{_{0}}D_{t}^{\alpha}(_{0}D_{t}^{\alpha}u(t)) &= f(t,u(t), {_{0}}D_{t}^{\alpha}u(t)), \quad t\in [0,1],\\ u(0) &= u(1) = 0. \end{align*} The existence of a nontrivial solution is stated through an iterative method based on mountain pass techniques.

Keywords

MathematicsLangevin equationApplied mathematicsMathematical physicsMathematical analysisStatistical physicsPhysics

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