Theory and Modern Applications
Page 39 of 98
This work explores the new exact solutions of nonlinear fractional partial differential equations (FPDEs). The solutions are obtained by adopting an effective technique, the first integral method (FIM). The Ri...
In this paper, we give a generalization of normal curves to n-dimensional Euclidean space. Then we obtain a necessary and sufficient condition for a curve to be a normal curve in the n-dimensional Euclidean space...
In this article, by using nonlinear Leray–Schauder-type alternative and Banach’s fixed point theorem, we investigate existence and uniqueness of solutions. We also prove Hyers–Ulam stability for the proposed c...
In this paper, we study a delayed predator–prey model with impulse and, in particular, the existence of the predator-free periodic solution. We employ the approach and techniques coming from epidemiology and c...
In this manuscript, we prove new aspects for several Opial-type integral inequalities for the left and right Caputo–Fabrizio operators with nonsingular kernel. For this purpose we use the inequalities obtained...
In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of di...
In this paper, we propose a numerical scheme for a system of two linear singularly perturbed parabolic convection-diffusion equations. The presented numerical scheme consists of a classical backward-Euler sche...
Based on a continuation theorem of Mawhin, the existence of a periodic solution for a higher-order nonlinear neutral difference equation is studied. Our conclusion is new and interesting.
In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. M...
In this paper, we obtain two approximations in law of the complex fractional Brownian motion by processes constructed from a Poisson process and a Lévy process, respectively.
A finite difference scheme, based upon the Crank–Nicolson scheme, is applied to the numerical approximation of a two-dimensional time fractional non-Newtonian fluid model. This model not only possesses a multi...
In this paper, we investigate the asymptotic behavior for a kind of resource competition model with environmental noises. Considering the impact of white noise on birth rate and death rate separately, we first...
In this paper, we consider fast convergent average consensus based on community detection algorithm. Generally, we know that a small network can have a faster convergence speed than a big one at the same condi...
In this paper, we define weak θ-contractions on a metric space into itself by extending θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014) and utilize the same to prove some fixed poin...
In this paper, we study the Hopf-zero bifurcation of Oregonator oscillator with delay. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, we get the normal form by per...
In this paper, stabilization is studied for a two-dimensional delta operator system with time-varying delays and actuator saturation. Both lower and upper bounds of the time-varying delays are considered. An e...
We consider the Kirchhoff-type p-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the Nehari method in critical point theory, we obtain the existence theorem of ...
We propose special difference problems of the four point scheme and the six point symmetric implicit scheme (Crank and Nicolson) for the first partial derivative of the solution ...
This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and di...
In this paper, we prove the existence and uniqueness of the equilibrium solution of the system by using the M-matrix and the topological degree technique and study the boundedness and robustness of dynamics of re...
In this paper, we consider a numerical solution for nonlinear advection–diffusion equation by a backward semi-Lagrangian method. The numerical method is based on the second-order backward differentiation formu...
In this paper, we introduce the concept of complete-closed time scales under translational and non-translational shifts and propose new definitions of special functions arising from dynamic equations on time s...
In this paper, we study the uniqueness problems of meromorphic functions and their difference operators. Our main result is a difference analogue of a result of Jank–Mues–Volkmann, which is concerned with the ...
In this article, we study a discrete fourth order boundary value problem. By making use of variational methods and critical point theory, we obtain some criteria for the existence and multiple solutions. Moreo...
In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simula...
This paper is devoted to an investigation of the multiple positive solutions to a class of infinite-point boundary value problems of nonlinear fractional differential equations coupled with the p-Laplacian ope...
In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier...
A three-species cooperative system with time delays and Lévy jumps is proposed in this paper. Firstly, by comparison method and inequality techniques, we discuss the stability in mean and extinction of species...
Considered herein is the periodic μ-Degasperis–Procesi equation, which is an evolution equation on the space of tensor densities over the Lie algebra of smooth vector fields. First two conditions on the initial d...
In this paper, based on the white noise theory for d-parameter Lévy random fields given by (Holden et al. in Stochastic Partial Differential Equations: A modeling, white noise functional approach, 2010), we devel...
We prove that approximations of derivations on random Banach ∗-algebras are exactly derivations by using a fixed point method. Furthermore, we show that approximations of quadratic ∗-derivations on random Bana...
This paper studies a class of asymptotically almost periodic recurrent neural networks involving mixed delays. By utilizing differential inequality analysis, some novel assertions are gained to validate the as...
In this manuscript, we investigate a sort of fractional neutral integro-differential equations with impulsive outcomes and extend the formula of general solutions for the impulsive fractional neutral integro-d...
In this paper, we derive the compositions of the fractional derivatives with the Shukla function, a four-parameter Mittag-Leffler function. We investigate and compare the difference between the Riemann–Liouvil...
The purpose of this paper is to investigate the qualitative behavior of HIV dynamics models with immune impairment. The HIV particles infect both CD4+ T cells and macrophages. Both latently and actively infected ...
In this paper, we study the periodic boundary value problems for the coupled systems of fractional implicit differential equations. Basing on the coincidence degree theory, we establish the existence and uniqu...
This paper studies the robust adaptive control of fractional-order chaotic systems with system uncertainties and bounded external disturbances. Based on a proposed lemma, quadratic Lyapunov functions are used ...
This article focuses on a proportional-derivative (PD) feedback controller to control a Neimark–Sacker bifurcation for a Mackey–Glass system by the Euler method. It has been shown that the onset of the Neimark...
A Caputo–Fabrizio type fractional order mathematical model for the dynamics of pine wilt disease (FPWD) is presented. The basic properties of the model are investigated. The existence and uniqueness of the sol...
Hadamard fractional derivatives are nonlocal fractional derivatives with singular logarithmic kernel with memory, and hence they are suitable to describe complex systems. In this paper, sufficient conditions a...
In this paper, we mainly discuss the existence and uniqueness results of solutions to fractional differential equations with multi-strip boundary conditions. When the fractional order α becomes integer, the exist...
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