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.