Fan, Ruixiong Zhai, Chengbo
Published in
Advances in Difference Equations
This article investigates the existence and uniqueness of periodic solutions for a new system of differential equations. By employing fixed point theorems for increasing φ-(h,τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgr...
Ahmed, Idris Kumam, Poom Jarad, Fahd Borisut, Piyachat Sitthithakerngkiet, Kanokwan Ibrahim, Alhassan
Published in
Advances in Difference Equations
In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach...
Ahmadi, Zahra Lashkaripour, Rahmatollah Baghani, Hamid Heidarkhani, Shapour Caristi, Giuseppe
Published in
Advances in Difference Equations
In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto’s results with some conditions removed based on a new technique is the main objective of this paper. In addition, we...
Xu, Changjin Liao, Maoxin Li, Peiluan Yuan, Shuai
Published in
Advances in Difference Equations
We study the weighted pseudo almost periodic solutions of a Lasota–Wazewska system. With the aid of fixed point theory and differential inequality strategies, we give a set of new sufficient criteria that guarantee the existence and global exponential stability of weighted pseudo almost periodic solutions to a Lasota–Wazewska system. The obtained r...
Zafar, Rashida Rehman, Mujeeb ur Shams, Moniba
Published in
Advances in Difference Equations
In this paper a general framework is presented on some operational properties of Caputo modification of Hadamard-type fractional differential operator along with a new algorithm proposed for approximation of Hadamard-type fractional integral using Haar wavelet method. Moreover, a generalized Taylor expansion based on Caputo–Hadamard-type fractional...
Yao, Huazhen Zhang, Jianwen
Published in
Advances in Difference Equations
This paper is concerned with the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with additive white noise, for which the nonlinear damping has a critical cubic growth rate. By showing the pullback asymptotic compactness of the stochastic dynamic systems, we prove the existence of a random attractor in H01×L2\documentc...
Chen, Li Chen, Zhuoyu
Published in
Advances in Difference Equations
We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formulae for them. At the same time, we also obtain a new recurrence formula involving the Gauss sums and two-term exponential sums.
Alomari, A. K.
Published in
Advances in Difference Equations
In this paper, we investigate the Sumudu transforms and homotopy analysis method (S-HAM) for solving a system of fractional partial differential equations. A general framework for solving such a kind of problems is presented. The method can also be utilized to solve systems of fractional equations of unequal orders. The algorithm is reliable and ro...
Etemad, Sina Rezapour, Shahram Samei, Mohammad Esmael
Published in
Advances in Difference Equations
We review the existence of solutions for a three-point nonlinear q-fractional differential equation and also its related inclusion. In this way, we use α-ψ-contractions and multifunctions. Also, we provide two examples to illustrate our main results. Finally by providing some algorithms and tables, we give some numerical computations for the result...
Kashuri, Artion Iqbal, Sajid Liko, Rozana Gao, Wei Samraiz, Muhammad
Published in
Advances in Difference Equations
We introduce new operators, the so-called left and right generalized conformable fractional integral operators. By using these operators we establish new Hermite–Hadamard inequalities for s-convex functions and products of two s-convex functions in the second sense. Also, we obtain two interesting identities for a differentiable function involving ...
