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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Advanced Methods in the Fractional Calculus of Variations

Advanced Methods in the Fractional Calculus of Variations

Odzijewicz, Tatiana
Malinowska, Agnieszka B.
Torres, Delfim F. M.

Paperback

Series: Springerbriefs in Applied Sciences and Technology

Technology & EngineeringCalculusPhysics

ISBN10: 3319147552
ISBN13: 9783319147550
Publisher: Springer Nature
Published: Mar 6 2015
Pages: 135
Weight: 0.48
Height: 0.32 Width: 6.14 Depth: 9.21
Language: English

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.

The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler-Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm-Liouville problems.

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