Advanced Methods in the Fractional Calculus of Variations by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M.

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

This short provides a basic unifying point of view at the fractional calculus. It brings jointly result of numerous contemporary ways in generalizing the least motion precept and the Euler–Lagrange equations to incorporate fractional derivatives.

The dependence of Lagrangians on generalized fractional operators in addition to on classical derivatives is taken into account in addition to nonetheless extra normal difficulties during which integer-order integrals are changed by way of fractional integrals. normal theorems are got for different types of variational difficulties for which fresh effects constructed within the literature may be got as distinct instances. particularly, the authors provide worthwhile optimality stipulations of Euler–Lagrange style for the elemental and isoperimetric difficulties, transversality stipulations, and Noether symmetry theorems. The life of strategies is established lower than Tonelli sort stipulations. the consequences are used to turn out the life of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems.

Advanced equipment within the Fractional Calculus of diversifications is a self-contained textual content on the way to be necessary for graduate scholars wishing to profit approximately fractional-order platforms. The targeted factors will curiosity researchers with backgrounds in utilized arithmetic, regulate and optimization in addition to in sure parts of physics and engineering.

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