(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we investigate higher-order calculus using the conformable derivative and integral. We use a fractional variant of the calculus of variations to obtain the Euler-Lagrange equation. Our route integral quantization approach streamlines the procedure by integrating solely over canonical coordinates q, eliminating the requirement to integrate higher-order derivatives . In addition, we employ the conformable derivative to develop canonical conserved energy-momentum and Ostrogradsky’s Hamiltonian. Furthermore, we generalized the Hamilton formulation for higher order derivatives and applied this new formulation to obtained equations of motion for a one dimensional point particle.