A new approach on fractional variational problems and Euler-Lagrange equations

作者：Bahrami F; Fazli H^*; Akbarfam A Jodayree

来源：Communications in Nonlinear Science & Numerical Simulation, 2015, 23(1-3): 39-50.

DOI：10.1016/j.cnsns.2014.10.025

• Fractional calculus
• Fractional variational problems
• Variational solutions
• Riemann-Liouville initial and boundary conditions
• Fractional Euler-Lagrange equations

In this paper we generalize fractional variational problems in [a, b]. We allow for the possibility that functions in the space of solution for the optimization problem can blow up at boundary points. The appropriate fractional derivative spaces are introduced and a compact embedding theorem demonstrated. We prove the existence of minimizers for the variational problems which satisfy the Euler- Lagrange equations with Riemann- Liouville boundary conditions. Our method is based on the fractional calculus of variations. An example is given to illustrate the results.

• 出版日期2015-6