Perturbation theory is a systematic procedure for obtaining approximate solutions to the perturbed problem by building on the known exact solutions to the unperturbed case.

Fractional calculus is very helpful in expressing the perturbation effects related to many important physical problems, and compared with the ordinary quantum-mechanical treatment leads to an incomplete, but approximated description.

Inthispaper,perturbationeffects will be carried out and a Hamiltonian for one of these effects which is the delta-function perturbation effect is constructed. The relevant Schrödinger’s equation has then been set up, and solved. The perturbation effects are represented clearly in the resultant wave function.

Consequently, we shall confine our treatment in obtaining expressions for the eigenvalues and eigenfunctions. We shall illustrate the perturbation by considering its application to several physical problems.

nonconservative systems, fractional calculus, Lagrangian and Hamiltonian, perturbation theory.