2 edition of On a nonlinear Volterra integrodifferential equation. found in the catalog.
On a nonlinear Volterra integrodifferential equation.
|Series||Commentationes physico-mathematicae v. 38, nr. 2, Commentationes physico-mathematicae ;, v. 38, nr. 2.|
|LC Classifications||Q60 .F555 vol. 38, nr. 2|
|The Physical Object|
|Number of Pages||11|
|LC Control Number||74554654|
The book also contributes to the theories of abstract first and second order differential equations, as well as to the theories of higher order abstract differential equations and incomplete abstract Cauchy problems, which can be viewed as parts of the theory of abstract Volterra integro-differential equations only in its broad sense. () Analytical Study of Nonlinear Fractional-Order Integrodifferential Equation: Revisit Volterra's Population Model. International Journal of Differential Equations , () A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation.
Finally, the result is applied to prove the existence and uniqueness of a solution for a system of nonlinear integrodifferential equations. 1. Introduction. Volterra–Fredholm integro differential equations [1–10] appear in a number of physical models, and an important question is whether these equations can support periodic solutions. This. D. Costarelli and R. Spigler, A collocation method for solving nonlinear Volterra integro-differential equations of the neutral type by sigmoidal functions, J. Integral Equations Appl. 26(1) () 15– Crossref, ISI, Google Scholar; S. A.
Abstract: A variation of constants formula is developed for nonlinear Volterra integral and integro-differential equations. This formula is suited to the study of various perturbation problems for Volterra equations. (Author). Basic Volterra theory In Vito Volterra published the ﬁrst of his fundamental papers on integral equations. It contains the following fundamental result (which may be viewed as marking the beginning of Functional Analysis). Theorem Assume that the kernel K(t,s) of the linear Volterra integral equation u(t) = g(t) + Zt 0 K(t,s)u(s)ds.
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Existence Theory for Nonlinear Integral and Integrodifferential Equations. Authors (view affiliations) Donal O’Regan; Search within book. Front Matter. Pages i-ix Pages Existence Theory for Nonlinear Fredholm and Volterra Integrodifferential Equations.
Donal O’Regan, Maria Meehan. Pages Solution Sets of Abstract. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes.
This book is intended for. Using the ψ-Hilfer fractional derivative, we present a study of the Hyers–Ulam–Rassias stability and the Hyers–Ulam stability of the fractional Volterra integro-differential equation Cited by: Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts.
Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations.
This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.
In this paper, a wavelet numerical method for solving nonlinear Volterra integro-differential equations of fractional order is presented. The method is based upon Euler wavelet approximations.
The Euler wavelet is first presented and an operational matrix of fractional-order integration is derived. By using the operational matrix, the nonlinear fractional integro-differential equations are.
Download Citation | Volterra Integro-Differential Equations | Volterra studied the hereditary influences when he was examining a population growth model. The research work resulted in a specific. We establish the existence and uniqueness of solutions for a class of nonlinear Volterra integral and integro-differential equations using fixed-point theorems for a new variant of cyclic (φ, ψ, θ) -contractive mappings.
Nontrivial examples are given to support the usability of our results. MSCH10, 54H This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations.
The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nonlinear equations, giving some general. This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators.
J. Wei, T. TianNumerical solution of nonlinear volterra integro-differential equations of fractional order by the reproducing kernel method Appl Math. Controllability of nonlinear neutral Volterra integrodifferential systems Article (PDF Available) in The Journal of the Australian Mathematical Society Series B Applied Mathematics 36(01) July.
The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes.
Selected worked-through examples. Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds.
The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra. The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations.
A major part of the research is devoted to the study of various types of abstract (multi-term) fracti. Volterra Equations and Applications book. Volterra Equations and Applications. DOI link for Volterra Equations and Applications. Degenerate Nonlinear Volterra Integrodifferential Equations.
View abstract. chapter 9 | 6 pages On Nonlinear Filtering of Non-Gaussian Processes Through Volterra Series. The second edition of A First Course in Integral Equations integrates the newly developed methods with classical techniques to give modern and robust approaches for solving integral equations.
The manual accompanying this edition contains solutions to all exercises with complete step-by-step details. In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind. A linear Volterra equation of the first kind is = ∫ (,) ()where ƒ is a given function and x is an unknown function to be solved for.
A linear Volterra equation of the second kind is. equations (IDE) is presented in a book by Lakshmikantham and Rao . Existence theory of nonlinear IDEs is also discussed in . Recently, Kostic  discussed the theory of abstract Volterra integro-differential equations.
A-stable linear multi-step methods to solve Volterra IDEs (VIDE) are proposed by Matthys in . Abstract Volterra Integro-Differential Equations [Kostic, Marko] on *FREE* shipping on eligible orders. Abstract Volterra Integro-Differential EquationsFormat: Hardcover. Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts.
Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and.The main aim in this work is to obtain an integral inequality with a clear estimate on time scales. The obtained inequality is used as a tool to investigate some basic qualitative properties of solutions to certain nonlinear Volterra-Fredholm integrodifferential equations on time scales.O.
Abu Arqub, M. Al-Smadi, and S. Momani, “Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations,” Abstract and Applied Analysis, vol.Article ID16 pages,