The Schr¨odinger equations generated by q-Bessel operator in quantum calculus

Abstract

In this paper, we obtain exact solutions of a new modification of the Schrödinger equation related to the Bessel q -operator. The theorem is proved on the existence of this solution in the Sobolev-type space W_q²(R⁺_q ) in the q -calculus. The results on correctness in the corresponding spaces of the Sobolev-type are obtained. For simplicity, we give results involving fractional q -difference equations of real order a> 0 and given real numbers in q -calculus. Numerical treatment of fractional q -difference equations is also investigated. The obtained results can be used in this field and be supplement for studies in this field.