Euler–Lagrange Equations for Lagrangians Containing Complex-order Fractional Derivatives

Teodor M. Atanacković (), Marko Janev (), Stevan Pilipović () and Dušan Zorica ()
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Teodor M. Atanacković: University of Novi Sad
Marko Janev: Serbian Academy of Arts and Sciences
Stevan Pilipović: University of Novi Sad
Dušan Zorica: Serbian Academy of Arts and Sciences

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 1, No 17, 256-275

Abstract: 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; 49K05; 49K15; 70G75; 70H03 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0873-6

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