Optimality Necessary Conditions For Continuous and discontinuous Fractional order Variational Problems

In this thesis, some properties and basic definitions of fractional integral and derivatives of Riemann-Liouvill
are presented , to construct the optimality conditions of mixed order unconstrained and constrained variational
problems with continuous and discontinuous functional, on fixed and moving boundaries ,based on the classical
product rule for Riemann-Liouvill , Several tested example are presented to demonstrate the implementation of the optimality necessary conditions.