Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Zorica, Dušan 
Title: Euler–Lagrange Equations for Lagrangians Containing Complex-order Fractional Derivatives
Journal: Journal of Optimization Theory and Applications
Volume: 174
Issue: 1
First page: 256
Last page: 275
Issue Date: 25-Jan-2017
Rank: M21
ISSN: 0022-3239
DOI: 10.1007/s10957-016-0873-6
Abstract: 
Two variational problems of finding the Euler–Lagrange equations corresponding to Lagrangians containing fractional derivatives of real- and complex-order are considered. The first one is the unconstrained variational problem, while the second one is the fractional optimal control problem. The expansion formula for fractional derivatives of complex-order is derived in order to approximate the fractional derivative appearing in the Lagrangian. As a consequence, a sequence of approximated Euler–Lagrange equations is obtained. It is shown that the sequence of approximated Euler–Lagrange equations converges to the original one in the weak sense as well as that the sequence of the minimal values of approximated action integrals tends to the minimal value of the original one.
Keywords: Complex-order fractional variational problems | Euler–Lagrange equations | Expansion formula | Weak convergence
Publisher: Springer Link
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 
Secretariat for Science of Vojvodina, Grant 114-451-947

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