We propose a novel algorithmic method for constructing invariant variational schemes of systems ordinary differential equations that are the Euler–Lagrange principle. The is based on invariantization standard, noninvariant discrete Lagrangian functionals using equivariant moving frames. given by corresponding invariantized functionals. showcase this general preserve and divergence symmetries as...

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit solution.

  In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems