On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative - Shaimardan, S.; Tokmagambetov, N.S. (KU Publ., 2021)
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.
Кейбір Риман-Лиувиль бөлшек q-туындылы q-бөлшек дифференциалдық теңдеулердің шешімдері туралы
О решениях некоторых q-дробных дифференциальных уравнений с дробных q-производными Римана-Лиувилля
Keywords: Cauchy type q-fractional problem; existence; uniqueness; q-derivative; q-calculus; fractional calculus; Riemann–Liouville fractional derivative; q-fractional derivative