Open AccessThe Schrödinger equations generated by q-Bessel operator in quantum calculus
Author(s) -
Serikbol Shaimardan,
N.S. Tokmagambetov
Publication year - 2022
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2022m1/102-108
Subject(s) - mathematics , sobolev space , bessel function , fractional calculus , operator (biology) , correctness , type (biology) , space (punctuation) , field (mathematics) , order (exchange) , schrödinger equation , mathematical analysis , pure mathematics , calculus (dental) , medicine , ecology , biochemistry , chemistry , linguistics , philosophy , dentistry , finance , repressor , algorithm , biology , transcription factor , economics , gene
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^2_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.