In this paper, we aim to study the dynamical behaviour of motion for a simple pendulum with mass decreasing exponentially in time. To examine interesting system, firstly obtain classical Lagrangian and Euler-Lagrange equation accordingly. Later, generalized is constructed via non-integer order derivative operators. The corresponding derived, calculated approximate results are simulated respect ...

This paper gathers the tools for solving Riemann-Liouville time fractional non-linear PDE’s by using a Galerkin method. method has advantage of not being more complicated than one used to solve same PDE with first order derivative. As model problem, existence and uniqueness is proved semilinear heat equations polynomial growth at infinity.

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...