Existence of a weak solution for fractional Euler-Lagrange equations

By Loïc Bourdin. 2012

67 citations recorded by the source corpus.

In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $$ \dfrac{\partial L}{\partial x} (u,D^\alpha_- u,t) + D^\alpha_+ (\dfrac{\partial L}{\partial y} (u,D^\alpha_- u,t)) = 0 $$ on a real interval $[a,b]$ and where $D^\alpha_-$ and $D^\alpha_+$ are the fractional derivatives of Riemann-Liouville of order $0 < \alpha < 1$.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b615216d13ddd064867a2faac4cae3bca0b8ddd7

Citations in the corpus

• A VARIATIONAL APPROACH FOR A PROBLEM INVOLVING A ψ-HILFER FRACTIONAL OPERATOR (2021, unknown): “Regarding other related works see [6, 8, 12,18,27,29,30,42,45,47,48].”
• Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, unknown): “We refer for example to [2, 6, 7, 9, 12, 21, 41, 43, 57] and references therein.”