相关论文: Abstract degenerate Volterra integro-differential …

In this paper, we are primarily concerned with the study of entire and analytical solutions of abstract degenerate (multi-term) fractional differential equations with Caputo time-fractional derivatives. We also analyze systems of such…

In this paper, for a degenerate higher order equation with a fractional derivative in the sense of Caputo, a nonlocal problem with conjugation conditions in a rectangular domain is studied. The solution is constructed in the form of a…

We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of…

In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $\alpha\in(0,1]$, and discuss the continuity of the respective solutions regarding the parameter $\alpha$. I also present a study about the…

In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1.…

This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one…

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the…

This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

The inverse nodal problem for Dirac differential operator perturbated by a Volterra integral operator is studied. We prove that dense subset of the nodal points determines the coefficients of differential and integral part of the operator.…

In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…

We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for…

In this paper, we investigate the abstract non-scalar Volterra difference equations. We employ the Poisson like transforms to connect the solutions of the abstract non-scalar Volterra integro-differential equations and the abstract…

In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…

The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular…

In this paper, we study backward stochastic Volterra integral equations of type-I with time delayed generators. Under some condition (small time horizon or a Lipschitz constant), we derive an existence and uniqueness results. Next, with the…

Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for…

In the article, in a rectangular domain, by the Fourier method, the initial boundary value problem for a high-order equation with two lines of degeneracy with a fractional derivative in the sense of Caputo is investigated for uniqueness and…

Given a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of…

We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces