Variational problems with fractional derivatives: Euler–Lagrange equations

By Teodor M. Atanackovic, Sanja Konjik, Stevan Pilipovic. 2008

177 citations recorded by the source corpus.

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler–Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler–Lagrange equations which approximate the initial Euler–Lagrange equations in a weak sense.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/004aaee483a2997066bc85a172014c388bdd7508

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[243] T.”
Fractional calculus of variations for a combined Caputo derivative (2011, background): “, [1, 5, 8, 12, 17, 19]), the Caputo fractional derivative (see, e.”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, background): “Fractional calculus of variation formulation The problems in fractional calculus of variation can be defined in terms of Caputo fractional derivatives as follows (see Almeida and Torres, 2009; Atanacković et al., 2008): let F be a function with continuous first and second (partial) derivatives with ”