Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces

By Rico Zacher. 2009

172 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e8c42bc41806d3ee8f19ed891268191ea3ea29f9

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

The General Fractional Derivative and Related Fractional Differential Equations (2020, background): “In [8,9], the properties of the appropriate defined weak solutions to the linear and quasi-linear evolutionary partial integro-differential equations of second order with the time-operators of type (13) in the form (Dk u)(t) = d dt ∫ t 0 k(t− τ)(u(τ)− u0) dτ, t ∈ R+ (15) were addressed in the case o”
An $L_q(L_p)$-theory for the time fractional evolution equations with variable coefficients (2015, methodology): “The results of [8, 33, 46] are operator theoretic, [21] is based on H-functional calculus, and the method of [47, 38] works well only in the Hilbert-space framework.”
L-estimates for time fractional parabolic equations with coefficients measurable in time (2018, background): “For divergence type time fractional parabolic equations in the Hilbert space setting, see [13], where the time fractional derivative is a generalized version of the Caupto fractional derivative.”
Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative (2016, background): “We note that such a trace problem was not considered in [42]; moreover, assumptions of [42] seem to be too weak to get necessary regularity.”
Fractional derivatives and the fundamental theorem of fractional calculus (2020, background): “These discussions mainly concerned the ”new fractional integrals and derivatives” ( [6, 8, 20, 24–26]), the integro-differential operators of convolution type with some general kernels ( [8, 14, 15, 24, 27, 28]), and the abstract axioms of FC ( [11, 19, 22]).”
Representation of solutions and large-time behavior for fully nonlocal diffusion equations (2015, background): “We recall that existence and uniqueness of weak solutions in Fα(T ) has been studied in [47], even in a more general context.”
Time fractional diffusion equations: solution concepts, regularity, and long-time behavior (2019, methodology): “[54]) and can be slightly improved in the time fractional case.”