A generalization of the concept of \(q\)-fractional integrals

DOI10.1007/S10114-009-8253-XzbMath1180.33026OpenAlexW1981680667MaRDI QIDQ1044337

Sladjana D. Marinković, Miomir S. Stanković, Predrag M. Rajković

Publication date: 11 December 2009

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-009-8253-x

zbMATH Keywords

Mittag-Leffler function\(q\)-derivativebasic hypergeometric functionsfractional integrals\(q\)-integral

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Basic hypergeometric integrals and functions defined by them (33D60)

Related Items (13)

Variational methods for fractional \(q\)-Sturm-Liouville problems ⋮ Fractal dimensions of fractional integral of continuous functions ⋮ On fractional \(q\)-Sturm-Liouville problems ⋮ Some new fractional \(q\)-integral Grüss-type inequalities and other inequalities ⋮ New developments on Ostrowski type inequalities via \(q\)-fractional integrals involving \(s\)-convex functions ⋮ PROGRESS ON ESTIMATION OF FRACTAL DIMENSIONS OF FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS ⋮ Some new fractional quantum integral inequalities ⋮ Fractional quantum integral operator with general kernels and applications ⋮ Some iterated fractional \(q\)-integrals and their applications ⋮ Fractional quantum integral inequalities ⋮ Some inequalities involving fractional \(q\)-derivatives related to the \(q\)-Leibniz rule ⋮ q-Laguerre polynomials and related q-partial differential equations ⋮ Analytical properties of \((q, k)\)-Mittag Leffler function

Cites Work

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• A fractional Leibniz q-formula
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Variational calculus on \(q\)-nonuniform lattices
• Algorithms for \(q\)-hypergeometric summation in computer algebra
• Weighted weak-type estimates for multilinear commutators of fractional integrals on spaces of homogeneous type
• Multilinear singular and fractional integrals
• The fractional derivatives of a fractal function
• q-Analogues of Cauchy's Formulas
• Some Fractional q-Integrals and q-Derivatives

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