Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations [PDF]
, 2007 Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that
Diethelm, Kai
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On the properties of the solution set map to Volterra integral inclusion
, 2017 For the multivalued Volterra integral equation defined in a Banach space, the set of solutions is proved to be $R_\delta$, without auxiliary conditions imposed in Theorem 6 [J. Math. Anal. Appl. 403 (2013), 643-666]. It is shown that the solution set map,
Pietkun, Radosław
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SMOOTH SOLUTIONS OF VOLTERRA EQUATIONS VIA SEMIGROUPS
, 2008 In this paper we introduce a class of left shift semigroups that are differentiable. With the help of perturbation theory for differentiable semigroups we show that solutions of an integrodifferential equation can be infinitely differentiable if the ...
T. Barta
semanticscholar +1 more source
The Harnack inequality for the Riemann-Liouville fractional derivation operator
, 2011 In this note we establish the Harnack inequality for the Riemann-Liouville fractional derivation operator ∂ t of order α ∈ (0, 1). Here the function under consideration is assumed to be globally nonnegative. We show that the Harnack inequality in general
Rico Zacher
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, 2018 In the first part of this work we show the convergence with respect to an asymptotic parameter {\epsilon} of a delayed heat equation. It represents a mathematical extension of works considered previously by the authors [Milisic et al. 2011, Milisic et al.
Milisic, Vuk, Oelz, Dietmar
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On the best constants in Markov-type inequalities involving Gegenbauer norms with different weights
, 2011 The paper is concerned with best constants in Markov-type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself.
A. Böttcher, P. Dörfler
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Properties of solutions for nonlinear Volterra integral equations [PDF]
, 2003 Some properties of non-locally bounded solutions for Abel integral equations are given. The case in which there exists two non-trivial solutions for such equations is also studied.
Arias, M. R., Benítez Suárez, Rafael
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Stationary dense operators in sequentially complete locally convex spaces
, 2018 The purpose of this paper is to investigate the stationary dense operators and their connection to distribution semigroups and abstract Cauchy problem in sequentially complete spaces.Comment: arXiv admin note: substantial text overlap with arXiv:1610 ...
c, Marko Kosti\' +2 more
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Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra-Fredholm Integral Equations. [PDF]
Int J Appl Comput Math, 2022 Pourdarvish A +3 more
europepmc +1 more source
Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise. [PDF]
Stoch Partial Differ Equ, 2023 Fahim K, Hausenblas E, Kovács M.
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