Volume 41, Issue 4

In the current paper, we consider a system of N -coupled weakly dissipative fractional nonlinear Schrödinger equations. The well-posedness of the initial value problem is established by a refined analysis based on a limiting argument as well as the study of the asymptotic dynamics of the solutions. This asymptotic behavior is described by the existence of a compact global attractor in the appropriate energy space.

New sufficient conditions for the oscillation of all solutions to a class of even-order differential equations with bounded and unbounded neutral coefficients are established, which refine, significantly simplify and generalize those in [T. Li and Y. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett. 61 2016, 35–41]. Examples are provided to illustrate the results and suggestions for future research are included.

We consider the sequential CFC-type nabla fractional difference ( CFC ∇ a + 1 ν ∇ a μ CFC u ) ( t ) {(^{\mathrm{CFC}}\nabla^{\nu}_{a+1}{}^{\mathrm{CFC}}\nabla^{\mu}_{a}u)(t)} and show that one can derive monotonicity-type results even in the case where this difference satisfies a strictly negative lower bound. This illustrates some dissimilarities between the integer-order and fractional-order cases.

We introduce the k -th almost Gauduchon condition on almost Hermitian manifolds. We show that if there is a k -th almost Gauduchon metric for some k , then it is k -th almost Gauduchon for any other k .

In this article, for the incomplete H -functions, we obtain a set of new generating functions. The bilateral along with linear generating relations are derived for the incomplete H -functions. Many of the generating functions readily accessible in the literature are often deemed as implementations of the main findings. All the derived findings are of a natural type and can produce a variety of new results in generating function theory.

By rewriting the relation 1 + 2 = 3 {1+2=3} as 1 2 + 2 2 = 3 2 {\sqrt{1}^{2}+\sqrt{2}^{2}=\sqrt{3}^{2}} , a right triangle is looked at. Some geometrical observations in connection with plane parqueting lead to an inductive sequence of right triangles with 1 2 + 2 2 = 3 2 {\sqrt{1}^{2}+\sqrt{2}^{2}=\sqrt{3}^{2}} as initial one converging to the segment [ 0 , 1 ] {[0,1]} of the real line. The sequence of their hypotenuses forms a sequence of real numbers which initiates some beautiful algebraic patterns. They are determined through some recurrence relations which are proper for being evaluated with computer algebra.

The prime objective of this paper is to define a new double difference operator with arbitrary order via which new classes of difference double sequences are introduced. Results on topological structures, dual spaces and four-dimensional matrix mappings related to the proposed difference double sequence spaces are discussed. As an application of this work, the proposed operator is being used to approximate partial derivatives of fractional orders. Some numerical examples are also given in support of the validity or the clear visualization of the results obtained.