A generalized \(q\)-fractional Gronwall inequality and its applications to nonlinear delay \(q\)-fractional difference systems

DOI10.1186/S13660-016-1181-2zbMath1353.39009OpenAlexW2526179128WikidataQ59460240 ScholiaQ59460240MaRDI QIDQ326432

Dumitru Baleanu, Thabet Abdeljawad, Jehad O. Alzabut

Publication date: 12 October 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-1181-2

zbMATH Keywords

numerical exampleuniqueness of solution\(q\)-Mittag-Leffler functionestimate for the solutiongeneralized \(q\)-fractional Gronwall inequalitynonlinear delay Caputo \(q\)-fractional difference system

Mathematics Subject Classification ID

Mittag-Leffler functions and generalizations (33E12) Difference equations, scaling ((q)-differences) (39A13) Other analytical inequalities (26D20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Gronwall's inequality on discrete fractional calculus
• \(q\)-fractional calculus and equations
• A generalized \(q\)-Mittag-Leffler function by \(q\)-Caputo fractional linear equations
• A new fractional integral inequality with singularity and its application
• Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies
• Discrete-time fractional variational problems
• Necessary optimality conditions for fractional difference problems of the calculus of variations
• Caputo \(q\)-fractional initial value problems and a \(q\)-analogue Mittag-Leffler function
• Continuity of solutions to discrete fractional initial value problems
• A generalized Gronwall inequality and its application to a fractional differential equation
• Modeling with fractional difference equations
• Nabla discrete fractional calculus and nabla inequalities
• Lagrange identity method for microstretch thermoelastic materials
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Symmetries of the \(q\)-difference heat equation
• Existence results for fractional \(q\)-difference equations with nonlocal \(q\)-integral boundary conditions
• The spectral problem for the \(q\)-Knizhnik-Zamolodchikov equation and continuous \(q\)-Jacobi polynomials
• Stability of \(q\)-fractional non-autonomous systems
• Fractional difference equations with real variable
• Generalized Gronwall inequalities and their applications to fractional differential equations
• The \(q\)-fractional analogue for Gronwall-type inequality
• A semigroup-like property for discrete Mittag-Leffler functions
• Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations
• A Comprehensive Treatment of q-Calculus
• Fractional q-Calculus on a time scale
• Initial value problems in discrete fractional calculus
• Inequalities for fractional differential equations
• Transformation theory of the q-oscillator
• Quantum symmetries of q-difference equations
• The q-Coulomb problem

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