On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative
Кейбiр Риман-Лиувиль бөлшек q-туындылы q-бөлшек дифференциалдық теңдеулердiң шешiмдерi туралы
О решениях некоторых q-дробных дифференциальных уравнений с дробными q-производными Римана–Лиувилля
Shaimardan S. Tokmagambetov N.S.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#104Issue 4130 - 141 pp.
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.
Cauchy type q-fractional problem , existence , fractional calculus , q-calculus , q-derivative , q-fractional derivative , Riemann–Liouville fractional derivative , uniqueness
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L.N. Gumilyev Eurasian National University, Nur-Sultan, Kazakhstan
Karagandy University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
L.N. Gumilyev Eurasian National University
Karagandy University of the name of academician E.A. Buketov
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026