Existence uniqueness and stability of mild solutions for semilinear \(\psi\)-Caputo fractional evolution equations

DOI10.1186/s13662-020-02570-8zbMath1482.34035OpenAlexW3032236432MaRDI QIDQ2057468

Parinya Sa Ngiamsunthorn, Apassara Suechoei

Publication date: 6 December 2021

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-020-02570-8

zbMATH Keywords

existence and uniqueness theoremsmeasure of noncompactnessmild solutionfractional evolution equationMittag-Leffler-Ulam-Hyers stability

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Fractional derivatives and integrals (26A33) Nonlinear differential equations in abstract spaces (34G20) Fractional ordinary differential equations (34A08) Measures of noncompactness and condensing mappings, (K)-set contractions, etc. (47H08)

Related Items

Semilinear fractional evolution inclusion problem in the frame of a generalized Caputo operator, Optimal feedback control for fractional evolution equations with nonlinear perturbation of the time-fractional derivative term, Unnamed Item, Approximate controllability of Ψ‐Caputo fractional differential equation, Unnamed Item, Existence, uniqueness, and Mittag-Leffler-Ulam stability results for Cauchy problem involving \(\psi \)-Caputo derivative in Banach and Fréchet spaces, Existence results to a \(\psi\)-Hilfer neutral fractional evolution equation with infinite delay, Existence uniqueness of mild solutions for \(\psi \)-Caputo fractional stochastic evolution equations driven by fBm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the initial value problem of fractional evolution equations with noncompact semigroup
• Fractional resolvents and fractional evolution equations
• Mittag-Leffler-Ulam stabilities of fractional evolution equations
• Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
• On right fractional calculus
• A class of fractional evolution equations and optimal controls
• Abstract fractional Cauchy problems with almost sectorial operators
• A study on the mild solution of impulsive fractional evolution equations
• Nonlocal Cauchy problem for fractional evolution equations
• On fractional powers of generators of fractional resolvent families
• Existence of mild solutions for fractional neutral evolution equations
• On some fractional evolution equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Semigroups of linear operators and applications to partial differential equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractals and fractional calculus in continuum mechanics
• The fundamental solutions for fractional evolution equations of parabolic type
• A Caputo fractional derivative of a function with respect to another function
• A modified analytical approach with existence and uniqueness for fractional Cauchy reaction-diffusion equations
• A new fractional modelling and control strategy for the outbreak of dengue fever
• New aspects of time fractional optimal control problems within operators with nonsingular kernel
• Generalized fractional derivatives and Laplace transform
• Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces
• On the analysis of vibration equation involving a fractional derivative with Mittag‐Leffler law
• On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions
• One-Parameter Semigroups for Linear Evolution Equations
• On generalized fractional operators and a gronwall type inequality with applications
• A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
• A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator
• A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence
• Stability of functional equations in several variables