Euler-lagrange Equations For Fractional Variational Problems

This thesis introduces three new operators and presents some of theirrnproperties. It defines a new class of variational problems in terms of thesernoperators and derives Euler-Lagrange equations for this class of problems. Itrnis demonstrated that the left and the right fractional Riemann-Liouvillernintegrals, and the left and the right fractional Riemann-Liouville, Caputo,rnRiesz-Riemann-Liouville and Riesz-Caputo derivatives are special cases ofrnthese operators, and they are obtained by considering a special kernel.rnFurther, the Euler-Lagrange equations developed for functional defined inrnterms of the left and the right fractional Riemann-Liouville, Caputo, Riesz-rnRiemann-Liouville and Riesz-Caputo derivatives are special cases of the Euler-rnLagrange equations developed here. Examples are considered to demonstraternthe applications of the new operators and the new Euler-Lagrange equations

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