In the present paper we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional implicit differential equations. An example is presented.

We adopt the following convention: x, y are real numbers, i, j, k are natural numbers, and p, q are finite sequences of elements of R. The following propositions are true: (1) Let A be a closed-interval subset of R and D be an element of divsA. If vol(A) 6= 0, then there exists i such that i ∈ domD and vol(divset(D, i)) > 0. (2) Let A be a closed-interval subset of R, D be an element of divsA, ...

Two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived, and the infinitely many conservation laws of the first integrable model is obtained. Moreover, the Darboux transformations based on different Darboux matrixes (2.3.4) and (3.2.4) for the above-mentioned integrable hierarchies are established with the help of two different gauge transformations ...

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...

The iterations are studied of the Darboux transformation for the generalized Schrödinger operator. The applications to the Dym and Camassa-Holm equations are considered.