We consider two evolution equations involving the space fractional Laplace operator of order 0<s<1 . We first establish some existence and uniqueness results for the considered evolution equations. Next, we give some comparison theorems and prove that, if the data of each equation are data bounded, then the solutions are also bounded.

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate operators by applying our weight functions. The key idea of deriving our error estimates is to divide the integration region into a ring-shaped area and some areas. In the appendix, we give an exemplary application of the main results of this paper.

This paper deals with the existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-metric spaces with initial and nonlocal conditions. The arguments are based on some fixed point theorems. Furthermore, two illustrations are presented to demonstrate the plausibility of our results.

Natural phenomena as well as problems encountered in pure and applied sciences are modeled by ordinary, partial or integral differential equations. Most of these problems have a nonlinear aspect which makes their studies difficult, or even impossible. For this, they must resort to other alternatives; among the methods used is the integral inequalities approach, which allows the study of quantitative and qualitative properties of solutions such as existence, uniqueness, delimitation, oscillation, and stability. In this study, we present some new integral inequalities of the Gronwall–Bellman–Bihari type associated with the fractional derivative of ψ-Hilfer, which represents a strong tool and is applicable in the study of certain differential equations. Several known results are derived and some applications to ordinary differential equations are provided to demonstrate the effectiveness of our finding.

We study the behavior of solutions of the Cauchy problem for a semi-linear heat equation with critical non-linearity in the sense of Joseph and Lundgren. It is known that if two solutions are initially close enough near the spatial infinity, then these solutions approach each other. In this paper, we give a universal lower bound of the convergence rate of solutions for a class of initial data. This rate contains a logarithmic term, which is not contained in the super critical non-linearity case. Proofs are given by a comparison method based on matched asymptotic expansion.

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.

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.

This paper deals with the evaluation of certain integral transforms involving the product of certain Appell and Bessel functions with a weight e-γ⁢t2 . The transformations of these integrals are evaluated in terms of the Appell, Kampé de Fériet and the triple hypergeometric functions. As an application, we studied propagation of generalized Humbert–Gaussian beams (GHGBs) and hypergeometric-Gaussian beams (HyGGBs) in turbulent atmosphere and through an ABCD paraxial optical system. The evaluation of these integral transforms has initiated a great interest in mathematical physics and its applications to laser physics and linear or non-linear optics.

In this study, we propose an inertial extragradient algorithm for solving a split generalized equilibrium problem as well as a split feasibility and common fixed point problem. We demonstrate that, under certain reasonable assumptions, the sequences induced by the proposed algorithm converge strongly to a solution of the corresponding problem. In addition, with the help of a numerical example, we demonstrate the efficiency of proposed algorithm. As a result of this paper, some recent well-known results in this area have been improved, generalized, and extended.

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.