Volume 43, Issue 3

First, we consider a non-trivial Einstein-type equation on a Kenmotsu manifold M and show that either M is Einstein or the potential function is pointwise collinear with ξ on an open set 𝒰 {\mathcal{U}} of M . Finally, we study an Einstein-type equation on an almost Kenmotsu ( κ , μ ) ′ {(\kappa,\mu)^{\prime}} -manifold.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane with respect to time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

The main crux of this work is to study the existence of solutions for a certain type of nonlinear Ψ-Caputo fractional differential equations with anti-periodic boundary conditions and p -Laplacian operator. The proofs are based on the Leray–Schauder degree theory and some basic concepts of Ψ-Caputo fractional calculus. As an application, our theoretical result has been illustrated by providing a suitable example.

The main object of this paper is to propose a new class of the Hermite-based polynomials by considering the Wiman (generalized Mittag-Leffler) function. We also indicate some analytical properties of our defined polynomials in a well-ordered way. Moreover, we consider a multi-index generalization of our generalized Hermite-based polynomials in the last section.

In this paper, we prove that for n 2 - 1 2 < α < n 2 {\frac{n}{2}-\frac{1}{2}<\alpha<\frac{n}{2}} , α ∉ ℕ {\alpha\notin\mathbb{N}} , the convolution operator S α ⁢ f ⁢ ( x ) = ∫ | y | ≥ 1 f ⁢ ( x - y ) ⁢ ( | y | 2 - 1 ) - α ⁢ 𝑑 y S_{\alpha}f(x)=\int_{|y|\geq 1}f(x-y)(|y|^{2}-1)^{-\alpha}\,dy is bounded from L p {L^{p}} to L q 1 + L q 2 {L^{q_{1}}+L^{q_{2}}} for certain values of p and q 1 , q 2 {q_{1},q_{2}} .