Euler-Lagrange Equations for Fractional variational problems
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Date
2017-09
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Addis Ababa University
Abstract
This thesis introduces three new operators and presents some of their
properties. It defines a new class of variational problems in terms of these
operators and derives Euler-Lagrange equations for this class of problems. It
is demonstrated that the left and the right fractional Riemann-Liouville
integrals, and the left and the right fractional Riemann-Liouville, Caputo,
Riesz-Riemann-Liouville and Riesz-Caputo derivatives are special cases of
these operators, and they are obtained by considering a special kernel.
Further, the Euler-Lagrange equations developed for functional defined in
terms of the left and the right fractional Riemann-Liouville, Caputo, Riesz-
Riemann-Liouville and Riesz-Caputo derivatives are special cases of the Euler-
Lagrange equations developed here. Examples are considered to demonstrate
the applications of the new operators and the new Euler-Lagrange equations
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Euler-Lagrange Equations