Weighted pseudo almost automorphic classical solutions and optimal mild solutions for fractional differential equations and application in fractional reaction-diffusion equations

DOI10.1007/s10910-014-0373-6zbMath1307.34006OpenAlexW2089925851MaRDI QIDQ460956

Junfei Cao, Caibin Zeng, Zaitang Huang

Publication date: 9 October 2014

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-014-0373-6

zbMATH Keywords

existence and uniquenessfractional differential equationfractional reaction-diffusion equationoptimal mild solutionweighted pseudo-almost automorphic classical solution

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Applications of operator theory to differential and integral equations (47N20) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (43A60) Fractional ordinary differential equations (34A08)

Related Items (8)

Existence of mild solutions for impulsive fractional integro-differential inclusions with state-dependent delay ⋮ EXISTENCE OF <i>µ</i>-PSEUDO ALMOST AUTOMORPHIC SOLUTIONS TO ABSTRACT PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY ⋮ Optimality of fractional impulsive partial stochastic differential systems with analytic sectorial operators and controls ⋮ Existence of optimal mild solutions for multi-valued impulsive stochastic partial functional integrodifferential equations ⋮ Existence results for an impulsive fractional integro-differential equation with state-dependent delay ⋮ Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay ⋮ Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations ⋮ Abstract weighted pseudo almost automorphic functions, convolution invariance and neutral integral equations with applications

Cites Work

• Unnamed Item
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• Pseudo almost automorphic solutions of fractional order neutral differential equation
• Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential equations in Hilbert spaces
• Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order
• Existence of the mild solution for some fractional differential equations with nonlocal conditions
• Nonlocal Cauchy problem for abstract fractional semilinear evolution equations
• Traveling-wave solution of non-linear coupled reaction diffusion equation arising in mathematical chemistry
• Almost automorphic solutions to a class of semilinear fractional differential equations
• Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces
• On some classes of almost automorphic functions and applications to fractional differential equations
• Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces
• Existence of pseudo-almost automorphic solutions to some abstract differential equations with \(\mathbf S^p\)-pseudo-almost automorphic coefficients
• Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications
• Perturbation of a globally stable steady state and uniform persistence
• Existence, uniqueness and attractiveness of a pseudo almost automorphic solutions for some dissipative differential equations in Banach spaces
• Weighted pseudo almost automorphic functions and applications to abstract differential equations
• Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations
• Semigroups of linear operators and applications to partial differential equations
• A semilinear parabolic Volterra integrodifferential equation
• Geometric theory of semilinear parabolic equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Semilinear integro-differential equations with compact semigroups
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Pseudo almost periodic solutions of some differential equations
• The Wright functions as solutions of the time-fractional diffusion equation.
• Fractional differential equations driven by Lévy noise
• On Mittag-Leffler-type functions in fractional evolution processes
• Numerical approach to fast reactions in reaction-diffusion systems: Application to buffered calcium waves in bistable models
• Some probability densities and fundamental solutions of fractional evolution equations
• Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations
• Pseudo almost periodic solutions of some differential equations. II
• Mathematical modelling of enzyme kinetics reaction mechanisms and analytical solutions of non-linear reaction equations
• A fractional diffusion equation to describe Lévy flights
• Weighted pseudo almost automorphic solution of an integro-differential equation, with weighted Stepanov-like pseudo almost automorphic forcing term
• The wavelet methods to linear and nonlinear reaction-diffusion model arising in mathematical chemistry
• A pseudospectral method of solution of Fisher's equation
• Pseudo almost automorphic solutions for dissipative differential equations in Banach spaces
• Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution equations
• UNIFORM CONVERGENCE OF MONOTONE SEQUENCES OF FUNCTIONS
• Integration of Vector-Valued Pseudo-Almost Periodic Functions
• FRACTAL DESCRIPTION OF ANOMALOUS DIFFUSION IN DYNAMICAL SYSTEMS
• Topics in Almost Automorphy
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC AND ALMOST PERIODIC FUNCTIONS
• A NEW APPROACH TO ALMOST PERIODICITY
• Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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