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
Correct solvability of hyperbolic Volterra equations with kernels depending on the parameter [PDF]
arXiv, 2014 We study the correct solvability of an abstract functional differential equations in Hilbert space, which includes integro-differential equations describing evolution of thermal phenomena, heat transfer in materials with memory or sound propagation in viscoelastic media.
arxiv
Applications of the Bielecki renorming technique [PDF]
arXiv, 2020 The renorming technique allows one to apply the Banach Contraction Principle for maps which are not contractions with respect to the original metric. This method was invented by Bielecki and manifested in an extremely elegant proof of the Global Existence and Uniqueness Theorem for ODEs. The present paper provides further extensions and applications of
arxiv
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.
europepmc +1 more source
Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
, 2001 A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional ...
Podlubny, Igor
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Solvable cases of optimal control problems for integral equations [PDF]
arXiv, 2016 We present a number of cases of optimal control of Volterra and Fredholm integral equations that are solvable in the sense that the problem can be reduced to a solvable integral equation. This is conceptually analogous to the role of the Riccati differential system in the optimal control of ordinary differential equations.
arxiv
Existence and Uniqueness for Nonlinear Integro-Differential Equations in Real Locally Complete Spaces [PDF]
Scientiae Mathematicae Japonicae, vol. 76, no. 3, (2013), 395-400, 2020 We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector ...
arxiv
A free boundary problem-in time-for the spread of Covid-19. [PDF]
J Math Biol, 2023 Luckhaus S, Stevens A.
europepmc +1 more source
Linear Volterra backward stochastic differential equations [PDF]
arXiv, 2017 We present an explicit solution triplet $(Y, Z, K)$ to the backward stochastic Volterra integral equation (BSVIE) of linear type, driven by a Brownian motion and a compensated Poisson random measure. The process $Y$ is expressed by an integral whose kernel is explicitly given.
arxiv
Spectral analysis of Volterra integrodifferential equations with the kernels, depending on parameter [PDF]
arXiv, 2017 Spectral analysis of operator-functions which are the symbols of the abstract integrodifferential equations of the Gurtin-Pipkin is provided. These equations represent abstract wave equations disturbed by terms involving Volterra operators. Correct solvability in the Sobolev space $W_{2}^{2}((0, T), A^2)$, for arbitrary $T>0$, of that abstract ...
arxiv