Malinowska A. Advanced Methods in the Fractional Calculus...2015

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This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives.
Introduction
Fractional Calculus
Fractional Calculus of Variations
Standard Methods in Fractional Variational Calculus
Direct Methods in Fractional Calculus of Variations
Application to the Sturm–Liouville Problem
Conclusion