Browsing by Author "Hailu, Diriba"

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    Euler-Lagrange Equations for Fractional variational problems
    (Addis Ababa University, 2017-09) Hailu, Diriba; Goa, Mengistu (PhD)
    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