Theory and Modern Applications
Page 44 of 98
The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hyperge...
This work is dedicated to the study of existence and uniqueness of almost everywhere solution of a multidimensional mixed problem for one class of third order differential equations with nonlinear operator on ...
This paper presents of some new Wirtinger-type integral inequalities by using Bessel functions. We establish one weighted Wirtinger inequality.
Recently, several problems in mathematics, physics, and engineering have been modeled via distributed-order fractional diffusion equations. In this paper, a new class of time distributed-order and space fracti...
In this article, we first establish an existence and uniqueness result for a class of systems of nonlinear operator equations under more general conditions by means of the cone theory and monotone iterative te...
In the paper, we are concerned with the existence and the exponential asymptotic behavior of traveling waves for the delayed Volterra-type cooperative system with nonquasimonotone condition
In this paper, an HBV epidemic model that incorporates saturating incidence and age-structure in the exposed and infectious classes is proposed. We study the asymptotic smoothness of semi-flow generated by the...
In this paper, we give some results on entire functions that share one value with their difference operators. In particular, we prove the following result, which can be regarded as a difference analogue of a r...
In this paper, we present an existence criterion for multiple positive solutions of nonlinear neutral delay partial difference equations. Such equations can be regarded as a discrete analog of neutral delay pa...
The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the Fibonacci diff...
The objective of this paper is to study the dynamics of the stochastic ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting. For the autonomous system, suffici...
In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale p...
A Lotka–Volterra commensal symbiosis model with first species subject to the Allee effect is proposed and studied in this paper. Local and global stability property of the equilibria are investigated. An amazi...
In this paper, an attempt is being made to investigate a class of fractional Fourier integral operators on classes of function spaces known as ultraBoehmians. We introduce a convolution product and establish a...
In this paper, we prove the following result: Let f be a nonconstant meromorphic function of finite order, p be a nonconstant polynomial, and c be a nonzero constant. If f, ...
In this paper, we investigate oscillatory and asymptotic properties for a class of fractional order dynamic equations on time scales, where the fractional derivative is defined in the sense of the conformable ...
In this paper, a class of first-order neutral differential equations with time-varying delays and coefficients is considered. Some results on the existence of positive almost periodic solutions for the equatio...
In this paper, we study a kind of difference equations with Riemann–Liouville-like fractional difference. The results on existence and attractivity are obtained by using the Picard iteration method and Schaude...
This paper investigates the design of disturbance attenuating controller for memristive recurrent neural networks (MRNNs) with mixed time-varying delays. By applying the combination of differential inclusions,...
In this paper, an adaptive neural network (NN) synchronization controller is designed for two identical strict-feedback chaotic systems (SFCSs) subject to dead-zone input. The dead-zone models together with th...
This article presents the bifurcation and chaos phenomenon of the three-dimensional generalized Hénon map. We establish the existence and stability conditions for the fixed points of the system. According to t...
In this paper we consider the existence of positive solutions of nth-order Sturm–Liouville boundary value problems with fully nonlinear terms, in which the nonlinear term f involves all of the derivatives
In this article, the following boundary value problem of fractional differential equation with Riemann–Stieltjes integral boundary condition
In this work, we deal with two-point Riemann–Liouville fractional boundary value problems. Firstly, we establish a new comparison principle. Then, we show the existence of extremal solutions for the two-point ...
This paper deals with the effect of parameters on properties of positive solutions and asymptotic behavior of an unstirred chemostat model with the Beddington–DeAngelis (denote by B–D) functional response unde...
This paper is concerned with the two-point boundary value problems of a nonlinear fractional q-difference equation with dependence on the first order q-derivative. We discuss some new properties of the Green func...
In this paper, we consider a spectrally negative Markov additive risk process. Using the theory of Jordan chain, a compact formula of Parisian ruin probability is given. The formula depends only on the scale m...
In this paper, we propose an extrapolation full multigrid (EXFMG) algorithm to solve the large linear system arising from a fourth-order compact difference discretization of two-dimensional (2D) convection dif...
Our investigation deals with the stability and permanence of diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes and time-delay in two dimensions. Firstly, we prove that the so...
In this paper, we study a class of periodic discrete nonlinear Schrödinger equations with asymptotically linear nonlinearities, and prove the existence of ground state solutions (i.e., nontrivial solutions wit...
A spatiotemporal discrete predator–prey system is investigated for understanding the pattern self-organization on the route to chaos. The discrete system is modelled by a coupled map lattice and shows advectio...
In this paper, a new parallel algorithm for solving parabolic equations is proposed. The new algorithm includes two domain decomposition methods, each method is applied to compute the values at
A new kind of multiple stochastic optimal stopping problem is formulated and its associated recursive variational inequalities are derived. We show that these variational inequalities can be solved exactly in ...
In this paper, a May cooperative system with strong and weak cooperative partners is proposed. First, by using differential inequality theory, we obtain the permanence and non-permanence of the system. Second,...
We consider a uniform finite difference method on a Bakhvalov mesh to solve a quasilinear first order parameterized singularly perturbed problem with integral boundary conditions. Uniform first order error est...
On the basis of the error correction method developed recently, an algorithm, so-called error embedded error correction method, is proposed for initial value problems. Two deferred equations are used to approx...
Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hy...
The aim of this paper is to obtain some new oscillatory conditions for all solutions of nonlinear difference equation with non-monotone or non-decreasing argument
...It is well known that many important properties of μ-pseudo almost automorphic (periodic) functions are based on the translation invariance. In this paper we give a new result of the translation invariance with c...
A predator–prey model, with aged structure in the prey population and the assumption that the predator hunts prey of all ages, is proposed and investigated. Using the uniform persistence theory for infinite di...
The combined compact difference (CCD) scheme has better spectral resolution than many other existing compact or noncompact high-order schemes, and is widely used to solve many differential equations. However, ...
This paper deals with the oscillation criteria for the linear delay differential equations. We present new sufficient conditions for the oscillation of all solutions of such equations. The results improve and ...
In this paper, a fractional order SIR epidemic model with nonlinear incidence rate is presented and analyzed. First, we prove the global existence, positivity, and boundedness of solutions. The equilibria are ...
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