By Agnieszka B. Malinowska,Tatiana Odzijewicz,Delfim F.M. Torres
This short offers a basic unifying point of view at the fractional calculus. It brings jointly result of a number of contemporary techniques 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 besides nonetheless extra basic difficulties during which integer-order integrals are changed by way of fractional integrals. normal theorems are received for different types of variational difficulties for which fresh effects built within the literature could be bought as precise circumstances. particularly, the authors supply precious optimality stipulations of Euler–Lagrange style for the basic and isoperimetric difficulties, transversality stipulations, and Noether symmetry theorems. The lifestyles of strategies is tested lower than Tonelli style stipulations. the implications 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 adaptations is a self-contained textual content so as to be precious for graduate scholars wishing to profit approximately fractional-order platforms. The specified factors will curiosity researchers with backgrounds in utilized arithmetic, regulate and optimization in addition to in definite parts of physics and engineering.
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Extra info for Advanced Methods in the Fractional Calculus of Variations (SpringerBriefs in Applied Sciences and Technology)
Advanced Methods in the Fractional Calculus of Variations (SpringerBriefs in Applied Sciences and Technology) by Agnieszka B. Malinowska,Tatiana Odzijewicz,Delfim F.M. Torres