Related papers: Abstract non-scalar Volterra difference equations

We present two integrable discretisations of a general differential-difference bicomponent Volterra system. The results are obtained by discretising directly the corresponding Hirota bilinear equations in two different ways. Multisoliton…

A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…

In this note, we study the convergence from the discrete to the continuous non-linear Fourier transform. Relations between spectral problems and questions in complex function theory provide a new approach to the study of scattering problems…

This paper first propose a concept of Weyl double-measure pseudo-almost automorphic functions and examines their fundamental characteristics. Subsequently, employing fixed point theorems, we systematically investigate the existence and…

We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work…

We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density,…

In this work we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type-changing with Caputo fractional derivative in the parabolic part. We equivalently reduce…

Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…

We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.

In this paper, we consider the Cauchy-type problem (1.1) involving Hilfer-Hadamard-type fractional derivative for a nonlinear fractional differential equation. We prove an equivalence between the Cauchy-type problem (1.1) and Volterra…

We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.

We construct examples of variational bivectors that are not Poissonian.

We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also…

Under investigation in this paper is the fractional integrable and non-integrable discrete modified Korteweg-de Vries hierarchies. The linear dispersion relations, completeness relations, inverse scattering transform, and fractional soliton…

In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by…

Volterra's integral equations with local and nonlocal loads represent the novel class of integral equations that have attracted considerable attention in recent years. These equations are a generalisation of the classic Volterra integral…

In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…

Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…

In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced…

The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…