Jafari, H. Nemati, S. Ganji, R. M.
Published in
Advances in Difference Equations

In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To carry out the proposed scheme, we calculate the oper...

Manafian, Jalil Alimirzaluo, Elnaz Nadjafikhah, Mehdi
Published in
Advances in Difference Equations

In this article, by using the Herman–Pole technique the conservation laws of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(3+1)-$\end{document} ( 3 + 1 ) − Jimbo–...

Asma, Shabbir, Sana Shah, Kamal Abdeljawad, Thabet
Published in
Advances in Difference Equations

Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnosel...

Khan, Amir Zarin, Rahat Humphries, Usa Wannasingha Akgül, Ali Saeed, Anwar Gul, Taza
Published in
Advances in Difference Equations

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved ...

Antuña, Almudena Guirao, Juan L. G. López, Miguel A.
Published in
Advances in Difference Equations

Let f:R→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f: \mathbb{R}\rightarrow \mathbb{R}$\end{document} be a map and τ∈R+\documentclass[12pt]{minimal} \usepackage{am...

Kassim, Mohammed D. Abdeljawad, Thabet Ali, Saeed M. Abdo, Mohammed S.
Published in
Advances in Difference Equations

In this research paper, we intend to study the stability of solutions of some nonlinear initial value fractional differential problems. These equations are studied within the generalized fractional derivative of various orders. In order to study the solutions’ decay to zero as a power function, we establish sufficient conditions on the nonlinear te...

Belmor, Samiha Jarad, Fahd Abdeljawad, Thabet
Published in
Advances in Difference Equations

This research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wa...

Xiong, Yu Wu, Zhaoyan
Published in
Advances in Difference Equations

The impulsive synchronization of a fractional-order complex-variable network is investigated. Firstly, static impulsive controllers are designed and the corresponding synchronization criteria are derived. From the criteria, the impulsive gains can be calculated. Secondly, adaptive impulsive controllers are designed. Noticeably, the impulsive gains ...

Ansari, Iqrar Khan, Khuram Ali Nosheen, Ammara Pečarić, Ðilda Pečarić, Josip
Published in
Advances in Difference Equations

Taylor’s polynomial and Green’s function are used to obtain new generalizations of an inequality for higher order convex functions containing Csiszár divergence on time scales. Various new inequalities for some divergence measures in quantum calculus and h-discrete calculus are also established.

Kassim, Mohammed D. Abdeljawad, Thabet Shatanawi, Wasfi Ali, Saeed M. Abdo, Mohammed S.
Published in
Advances in Difference Equations

The aim of this article is to discuss the uniqueness and Ulam–Hyers stability of solutions for a nonlinear fractional integro-differential equation involving a generalized Caputo fractional operator. The used fractional operator is generated by iterating a local integral of the form (Iaρf)(t)=∫atf(s)sρ−1ds\documentclass[12pt]{minimal} \usepackage{a...