A note on the mild solutions of Hilfer impulsive fractional differential equations

DOI10.1016/J.CHAOS.2021.110944zbMath1486.34116arXiv1811.09256OpenAlexW3155152904WikidataQ115359164 ScholiaQ115359164MaRDI QIDQ2143576

D. S. Oliveira, J. Vanterler da Costa Sousa, Edmundo Capelas de Oliveira

Publication date: 31 May 2022

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

Full work available at URL: https://arxiv.org/abs/1811.09256

zbMATH Keywords

uniquenessmild solutionfractional differential equationsgeneralized Gronwall inequalityHilfer fractional derivative\(\delta\)-Ulam-Hyers-Rassias stability

Mathematics Subject Classification ID

Ordinary differential equations with impulses (34A37) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Perturbations of ordinary differential equations (34D10) Fractional ordinary differential equations (34A08)

Related Items (11)

Stability of mild solutions of the fractional nonlinear abstract Cauchy problem ⋮ Fractional Chebyshev deep neural network (FCDNN) for solving differential models ⋮ Almost sectorial operators on Ψ‐Hilfer derivative fractional impulsive integro‐differential equations ⋮ Convergence analysis of Riemann‐Liouville fractional neural network ⋮ Decay mild solutions of Hilfer fractional differential variational-hemivariational inequalities ⋮ The e-positive mild solutions for impulsive evolution fractional differential equations with sectorial operator ⋮ Caputo fractional differential variational-hemivariational inequalities involving history-dependent operators: global error bounds and convergence ⋮ Stability analysis for fractional order implicit ψ‐Hilfer differential equations ⋮ On the (k,Ψ)‐Hilfer nonlinear impulsive fractional differential equations ⋮ Discussion on existence of mild solutions for Hilfer fractional neutral stochastic evolution equations via almost sectorial operators with delay ⋮ Ulam-Hyers type stability for \(\psi\)-Hilfer fractional differential equations with impulses and delay

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