In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fourth kind, Wn(x)Wn(x), corresponding to respective weight functions View the MathML sourceW(1)(x)...

Quaternionic analysis is a branch of classical referring to different generalizations the Cauchy-Riemann equations quaternion skew field \(\mathbb H\) context. In this work we deals with H-\)valued \((\theta , u)-\)hyperholomorphic functions related elements kernel Helmholtz operator parameter \(u \in \mathbb H\), just in same way as usual quaternionic set harmonic functions. Given domain \(\Om...

In this work, we prove a comparison result for general class of nonlinear dispersive unidirectional wave equations. The nature one-dimensional waves occurs because convolution integral in space. For two specific choices the kernel function, Benjamin–Bona–Mahony equation and Rosenau that are particularly suitable to model water elastic waves, respectively, members class. We first an energy estim...

<p style='text-indent:20px;'>We consider nonlinear mutation selection models, known as <i>replicator-mutator</i> equations in evolutionary biology. They involve a nonlocal kernel and confining fitness potential. We prove that the long time behaviour of Cauchy problem is determined by principal eigenelement underlying linear operator. The novelties compared to literature on the...

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted,the density function is...

In this paper, we study left and right [Formula: see text]-regular functions that originally were introduced in [I. Frenkel M. Libine, Quaternionic analysis, representation theory physics II, accepted Adv. Theor. Math. Phys]. When text], these are the usual quaternionic regular functions. We show satisfy most of properties functions, including conformal invariance under fractional linear transf...

This article concerns the dynamical behavior for a reaction-diffusion equation with integral term. First, by using bifurcation analysis and center manifold theorem, existence of periodic steady-state solution are established special kernel function general respectively. Then, we prove model admits traveling wave solutions connecting this steady state to uniform u=1 applying reduction phase diag...