Published in Advances in Difference Equations
The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences um\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\o...
Published in Advances in Difference Equations
In this paper, we investigate the existence and uniqueness of a solution for a class of ψ-Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, and Krasnosellskii’s fixed point theorems. Further, applying the techniques of nonlinear functional analysis, we establis...
Published in Advances in Difference Equations
We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detail...
Published in Advances in Difference Equations
Let f be an entire function of finite order, let n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n\geq 1$\end{document}, m≥1\documentclass[12pt]{minimal} \usepackage{...
Published in Advances in Difference Equations
A Correction to this paper has been published: https://doi.org/10.1186/s13662-020-03199-3
Published in Advances in Difference Equations
In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial func...
Published in Advances in Difference Equations
We propose a new modification of homotopy perturbation method (HPM) called the δ-homotopy perturbation transform method (δ-HPTM). This modification consists of the Laplace transform method, HPM, and a control parameter δ. This control convergence parameter δ in this new modification helps in adjusting and controlling the convergence region of the s...
Published in Advances in Difference Equations
We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference method together with θ-weighted scheme. Then, for the approximation of spatial part of unknown function and its spatial derivatives, we use a mixe...
Published in Advances in Difference Equations
In this paper, we mainly study a kind of fractional-order multiple point boundary value problem involving noninstantaneous impulse and abstract bounded operator. The existence and uniqueness is obtained by the Banach contraction principle. And by applying direct analysis methods, we establish some conditions of the Ulam–Hyers stability for this pro...
Published in Advances in Difference Equations
We study the oscillation of a first-order linear delay differential equation. A new technique is developed and used to obtain new oscillatory criteria for differential equation with non-monotone delay. Some of these results can improve many previous works. An example is introduced to illustrate the effectiveness and applicability of our results.
