Existence of solutions of the abstract Cauchy problem of fractional order
DOI10.1016/j.jfa.2021.109028zbMath1469.34017OpenAlexW3147132982MaRDI QIDQ831106
Juan C. Pozo, Hernán R. Henríquez, Jaqueline Godoy Mesquita
Publication date: 10 May 2021
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2021.109028
mild solutionsclassical solutionsfractional abstract Cauchy problemfractional derivatives in Caputo sense
One-parameter semigroups and linear evolution equations (47D06) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Linear differential equations in abstract spaces (34G10) Nonautonomous smooth dynamical systems (37C60) Fractional ordinary differential equations (34A08)
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Cites Work
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- Relative controllability of linear systems of fractional order with delay
- A parabolic problem with a fractional time derivative
- Approximate controllability and optimal controls of fractional evolution systems in abstract spaces
- Decay estimates for time-fractional and other non-local in time subdiffusion equations in \(\mathbb R^d\)
- Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces
- Controllability of nonlocal fractional differential systems of order \(\alpha \in (1,2\) in Banach spaces]
- Topics in fractional differential equations
- Fractional resolvents and fractional evolution equations
- Porous medium flow with both a fractional potential pressure and fractional time derivative
- Mittag-Leffler functions and their applications
- Differential equations in Banach spaces. II: Theory of cosine operator functions
- Existence and uniqueness of solutions for a boundary value problem of fractional type with nonlocal integral boundary conditions in Hölder spaces
- Controllability of abstract systems of fractional order
- Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Functional analysis, Sobolev spaces and partial differential equations
- Semigroups of linear operators and applications to partial differential equations
- On Mittag-Leffler-type functions in fractional evolution processes
- Differentiability of solutions of the second order abstract Cauchy problem
- The optimal behavior of solutions to fractional impulsive stochastic integro-differential equations and its control problems
- A new approach for solving a class of delay fractional partial differential equations
- On spectral inclusions and approximations of \(\alpha\)-times resolvent families
- Solution existence for non-autonomous variable-order fractional differential equations
- Existence and uniqueness of mild solution for fractional integrodifferential equations
- Controllability problem of fractional neutral systems: a survey
- \(L_p\)-estimates for time fractional parabolic equations in divergence form with measurable coefficients
- Existence results for a generalization of the time-fractional diffusion equation with variable coefficients
- On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation
- Existence of solutions for some two-point fractional boundary value problems under barrier strip conditions
- Existence of the classical and strong solutions for fractional semilinear initial value problems
- An alpha-beta phase diagram representation of the zeros and properties of the Mittag-Leffler function
- Asymptotically periodic solutions for Caputo type fractional evolution equations
- Fractional rheological models for thermomechanical systems. Dissipation and free energies
- General fractional differential equations of order \(\alpha \in (1,2)\) and type \(\beta \in [0,1\) in Banach spaces]
- S-asymptotically \(\omega\)-periodic mild solutions of neutral fractional differential equations with finite delay in Banach space
- Existence of solutions and approximate controllability of fractional nonlocal neutral impulsive stochastic differential equations of order \(1<q<2\) with infinite delay and Poisson jumps
- Study on fractional non-autonomous evolution equations with delay
- Semilinear fractional differential equations with infinite delay and non-instantaneous impulses
- Functional impulsive differential equation of order α ∈(1,2) with nonlocal initial and integral boundary conditions
- Functional Fractional Calculus
- Vector-valued Laplace Transforms and Cauchy Problems
- Differentiability of Weak Solutions to an Abstract Inhomogeneous Differential Equation
- One-Parameter Semigroups for Linear Evolution Equations
- On S‐asymptotically ω‐periodic and Bloch periodic mild solutions to some fractional differential equations in abstract spaces
- Fractional Differential Equations
- The Green function of a linear differential equation with a lateral condition
- On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses
- Fractional Calculus: Integral and Differential Equations of Fractional Order
- Controllability for Impulsive Fractional Evolution Inclusions with State-Dependent Delay
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- On non-autonomous abstract nonlinear fractional differential equations
- On cosine operator functions and one-parameter groups of operators
- The random walk's guide to anomalous diffusion: A fractional dynamics approach