Ulam stability of Caputo \(q\)-fractional delay difference equation: \(q\)-fractional Gronwall inequality approach

DOI10.1186/s13660-019-2257-6zbMath1499.39073OpenAlexW2991649288WikidataQ126641783 ScholiaQ126641783MaRDI QIDQ2068099

Thabet Abdeljawad, Manar A. Alqudah, Rabia Ilyas Butt, Mujeeb Ur Rehman

Publication date: 19 January 2022

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

Full work available at URL: https://doi.org/10.1186/s13660-019-2257-6

zbMATH Keywords

existenceuniquenessdelay difference equationUlam-Hyers-Rassias stabilityUlam-Hyers stability\(q\)-fractional Gronwall inequality

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Difference equations, scaling ((q)-differences) (39A13) Stability theory for difference equations (39A30)

Related Items (14)

Ulam's type stability analysis of fractional difference equation with impulse: Gronwall inequality approach ⋮ Finite-time stability of \(q\)-fractional damped difference systems with time delay ⋮ A novel fractional structure of a multi-order quantum multi-integro-differential problem ⋮ Existence criteria via \(\alpha-\psi\)-contractive mappings of \(\phi\)-fractional differential nonlocal boundary value problems ⋮ On a nonlinear sequential four-point fractional \(q\)-difference equation involving \(q\)-integral operators in boundary conditions along with stability criteria ⋮ On two structures of the fractional q‐sequential integro‐differential boundary value problems ⋮ A DIFFERENCE METHOD FOR SOLVING THE NONLINEAR q-FRACTIONAL DIFFERENTIAL EQUATIONS ON TIME SCALES ⋮ Pata type contractions involving rational expressions with an application to integral equations ⋮ Investigating a class of pantograph differential equations under multi-points boundary conditions with fractional order ⋮ Criteria for existence of solutions for a Liouville-Caputo boundary value problem via generalized Gronwall's inequality ⋮ Ulam stability for nonautonomous quantum equations ⋮ An existence study on the fractional coupled nonlinear \(q\)-difference systems via quantum operators along with Ulam-Hyers and Ulam-Hyers-Rassias stability ⋮ The particular solution and Ulam stability of linear Riemann-Liouville fractional dynamic equations on isolated time scales ⋮ THE UNIQUE EXISTENCE OF SOLUTION IN THE q-INTEGRABLE SPACE FOR THE NONLINEAR q-FRACTIONAL DIFFERENTIAL EQUATIONS

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