Open AccessOn the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative
Author(s) -
Serikbol Shaimardan,
AUTHOR_ID,
N.S. Tokmagambetov,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m4/130-141
Subject(s) - fractional calculus , mathematics , time scale calculus , derivative (finance) , differential equation , order (exchange) , type (biology) , mathematical analysis , calculus (dental) , pure mathematics , multivariable calculus , medicine , ecology , finance , dentistry , control engineering , financial economics , engineering , economics , biology
This paper is devoted to explicit and numerical solutions to linear fractional q-difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q-derivative in q-calculus. The approaches based on the reduction to Volterra q-integral equations, on compositional relations, and on operational calculus are presented to give explicit solutions to linear q-difference equations. 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. Finally, some examples are provided to illustrate our main results in each subsection.