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 Schr¨odinger equation related to the Bessel q-operator. The theorem is proved on the existence of this solution in the Sobolev-type space W2 q (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.