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Measures of noncompactness in the study of solutions of infinite systems of Volterra-Hammerstein-Stieltjes integral equations
The paper is dedicated to investigate conditions guaranteeing the solvability of infinite systems of Volterra-Hammerstein-Stieltjes integral...
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Approximate Solution of the System of Linear Volterra–Stieltjes Integral Equations of the Second Kind
A numerical solution of the system of linear Volterra–Stieltjes integral equations of the second kind has been found and analyzed using the so-called...
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The origin and developments of Kurzweil’s generalized Riemann integral
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further...
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Dynamics of One-Dimensional Maps and Gurtin–Maccamy’s Population Model. Part I. Asymptotically Constant Solutions
Motivated by the recent work by Ma and Magal [Proc. Amer. Math. Soc. (2021); https://doi.org/10.1090/proc/15629 ] on the global stability property of...
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Nonlinear second order systems of Fredholm integro-differential equations
A large class of physical phenomena in biophysics, chemical engineering, and physical sciences are modeled as systems of Fredhold...
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Aspects of stochastic control theory
In the present chapter, we introduce linear stochastic control systems and the corresponding notions of stability, stabilizability and detectability....
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Linear Operators and Equations with Partial Integrals
We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, and spaces of continuous...
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The Wave Equation with Memory
In this chapter, we study wave front asymptotics of solutions of wave equations with memory. Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, and 3.9...
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Numerical analytic continuation
Let f be an analytic function on a simply-connected compact continuum E of the complex z -plane. This might be an interval of the real line, where f ...
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Attractivity for Differential Equations of Fractional order and ψ-Hilfer Type
This paper investigates the overall solution attractivity of the fractional differential equation involving the ψ -Hilfer fractional derivative and...
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Solvability of a nonlinear Volterra–Stieltjes integral equation in the class of bounded and continuous functions of two variables
The aim of this paper is to investigate the solvability of a nonlinear Volterra–Stieltjes integral equation in two variables in the space
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Atto-Foxes and Other Minutiae
This paper addresses the problem of extinction in continuous models of population dynamics associated with small numbers of individuals. We begin...
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Mathematical Preliminaries
This chapter presents most of the basic and important results from analysis required to read the book smoothly. It contains many relevant results...
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Commentaries and Further Developments
In this chapter, we comment on and discuss some of the most important further developments obtained in the domains considered. More extensions are...
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Transmutation Operators and Their Applications
We approach the subject of transmutations from the operator theoretic point of view and use them to compare general differential operators, and...
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Subordination in a Class of Generalized Time-Fractional Diffusion-Wave Equations
Motivated by recently proposed generalizations of the diffusion-wave equation with the Caputo time fractional derivative of order α ∈ (1, 2), in the...
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Testimonies
We contacted several researchers who worked on the topics treated in this book or related to them, and asked them for their testimony about the...
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Theory of Multidimensional Delsarte–Lions Transmutation Operators. I
We present a brief survey of the original results obtained by the authors in the theory of Delsarte–Lions transmutations of multidimensional spectral...
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Applications to Deterministic Models
Here we present material illuminating the role of the Mittag-Leffler function and its generalizations in the study of deterministic models. It has...