Related papers: Solutions around a Regular {\alpha} Singular Point…
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the…
A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For given evaluation point and equation parameters the memory requirement scales linearly with precision $P$, and the number…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for a hierarchy of integrable difference equations. We also provide an example of such a solution that is related to sequence generated…
The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian $L(x(t)$, where $_a^cD_t^\alpha x(t))$ and $0<\alpha< 1$, such that the following…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
We study the linear fractional Schr\"odinger equation on a Hilbert space, with a fractional time derivative of order $0<\alpha<1,$ and a self-adjoint generator $A.$ Using the spectral theorem we prove existence and uniqueness of strong…
We study the Cauchy problem for a general homogeneous linear partial differential equation in two complex variables with constant coefficients and with divergent initial data. We state necessary and sufficient conditions for the summability…
In this paper, we first discuss the convolution series that are generated by the Sonine kernels from a class of functions continuous on the real positive semi-axis that have an integrable singularity of power function type at the point…
In this paper we study stable solutions to the fractional equation \begin{align} (-\Delta)^s u =f(u), \quad |u| < 1 \quad \mbox{in $\mathbb{R}^d$}, \end{align}where $0<s<1$ and $f:[-1,1] \rightarrow \mathbb{R}$ is a $C^{1,\alpha}$ function…
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…
Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives…
In this paper, we consider a q-analogue of the Borel-Laplace summation where q>1 is a real parameter. In particular, we show that the Borel-Laplace summation of a divergent power series solution of a linear differential equation can be…
We show the existence of periodic solutions for continuous symmetric perturbations of certain planar power law problems.
The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of the numerical solutions of FDEs whose solutions are…
We consider a time fractional differential equation of order $\alpha$, $0<\alpha<1$, $$ \frac{\partial c(x,t)}{\partial t}={}^C_0\mathcal{D}_t^{\alpha}[(Ac)(x,t)]+q(x,t) ,\quad x > 0, t > 0, \quad c(x,0)=f(x). $$ where…