The Schr¨odinger equations generated by q-Bessel operator in quantum calculus - Shaimardan, S.; Tokmagambetov, N.S. (My University, 2022)
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.
Keywords: q-integral; q-Jackson integral; q-difference operator q-derivative; the q-Bessel Fourier transform; the Sobolev type space; the Schr¨odinger equation; q-Bessel operator