On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative

DOI10.1016/j.chaos.2018.10.006zbMath1442.34016OpenAlexW2897183705MaRDI QIDQ2201386

Zakia Hammouch, Fahd Jarad, Thabet Abdeljawad

Publication date: 29 September 2020

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2018.10.006

zbMATH Keywords

Gronwall inequalityUlam-Hyers stabilityAtangana-Baleanu fractional derivativesAtangana-Baleanu fractional integrals

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Stability of solutions to ordinary differential equations (34D20) Fractional ordinary differential equations (34A08)

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Cites Work

• Caputo-type modification of the Hadamard fractional derivatives
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• On Caputo modification of the Hadamard fractional derivatives
• A generalized Gronwall inequality and its application to a fractional differential equation
• Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels
• Monotonicity results for fractional difference operators with discrete exponential kernels
• Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel
• Fractional operators with exponential kernels and a Lyapunov type inequality
• Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws
• Discrete Mittag-Leffler kernel type fractional difference initial value problems and Gronwall's inequality
• Non validity of index law in fractional calculus: a fractional differential operator with Markovian and non-Markovian properties
• Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana-Baleanu derivative
• On the generalized fractional derivatives and their Caputo modification
• Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel
• On generalized fractional operators and a gronwall type inequality with applications
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