Advances in Difference Equations

Journal Information
ISSN / EISSN : 1687-1847 / 1687-1847
Current Publisher: Springer Science and Business Media LLC (10.1186)
Former Publisher: Hindawi Limited (10.1155)
Total articles ≅ 4,632
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Latest articles in this journal

, Dumitru Baleanu, Khaled Mohamed Khedher, Osama Moaaz
Advances in Difference Equations, Volume 2021, pp 1-20; doi:10.1186/s13662-021-03446-1

Abstract:
In this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results.
Monairah Alansari, Muhammad Usman Ali
Advances in Difference Equations, Volume 2021, pp 1-13; doi:10.1186/s13662-021-03443-4

Abstract:
In this article, we introduce two notions of interpolative F-contractions with shrink map and F-contractions with shrink map. We also study the existence of E-fixed points by using these notations on a metric space endowed with a binary relation. As an application and consequence of the main results, we also get some other interesting results like a common fixed point result, an E-fixed point result on a metric space equipped with graph, and an existence theorem for a solution of integral equations.
Rabha W. Ibrahim, Ibtisam Aldawish
Advances in Difference Equations, Volume 2021, pp 1-16; doi:10.1186/s13662-021-03442-5

Abstract:
Symmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator.
, Wenyan Tang
Advances in Difference Equations, Volume 2021, pp 1-16; doi:10.1186/s13662-021-03434-5

Abstract:
In this work, we present a lake-eutrophication model with nontransient/transient impulsive dredging and pulse inputting. We obtain globally asymptotically stable conditions for the phytoplankton-extinction periodic solution of system (2.1). Furthermore, we gain the permanent conditions for system (2.1). Finally, we employ computer simulations to illustrate the results. Our results indicate the effective controlling strategy for water resource management.
, Soha Hamdan, Ahmed Alsaedi, Sotiris K. Ntouyas
Advances in Difference Equations, Volume 2021, pp 1-21; doi:10.1186/s13662-021-03440-7

Abstract:
In this research we introduce and study a new coupled system of three fractional differential equations supplemented with nonlocal multi-point coupled boundary conditions. Existence and uniqueness results are established by using the Leray–Schauder alternative and Banach’s contraction mapping principle. Illustrative examples are also presented.
Bilal Khan, H. M. Srivastava, , Shahid Khan, Nazar Khan, Qazi Zahoor Ahmad
Advances in Difference Equations, Volume 2021, pp 1-14; doi:10.1186/s13662-021-03441-6

Abstract:
In the present paper, by using the concept of convolution and q-calculus, we define a certain q-derivative (or q-difference) operator for analytic and multivalent (or p-valent) functions. This presumably new q-derivative operator is an extension of the known q-analogue of the Ruscheweyh derivative operator. We also give some interesting applications of this q-derivative operator for multivalent functions by using the method of differential subordination. Relevant connections with a number of earlier works on this subject are also pointed out.
Ahmad Neirameh, Foroud Parvaneh
Advances in Difference Equations, Volume 2021, pp 1-28; doi:10.1186/s13662-021-03439-0

Abstract:
Exact solutions to nonlinear differential equations play an undeniable role in various branches of science. These solutions are often used as reliable tools in describing the various quantitative and qualitative features of nonlinear phenomena observed in many fields of mathematical physics and nonlinear sciences. In this paper, the generalized exponential rational function method and the extended sinh-Gordon equation expansion method are applied to obtain approximate analytical solutions to the space-time conformable coupled Cahn–Allen equation, the space-time conformable coupled Burgers equation, and the space-time conformable Fokas equation. Novel approximate exact solutions are obtained. The conformable derivative is considered to obtain the approximate analytical solutions under constraint conditions. Numerical simulations obtained by the proposed methods indicate that the approaches are very effective. Both techniques employed in this paper have the potential to be used in solving other models in mathematics and physics.
Jun-Ming Zhu,
Advances in Difference Equations, Volume 2021, pp 1-8; doi:10.1186/s13662-021-03433-6

Abstract:
In this paper, by constructing contour integral and using Cauchy’s residue theorem, we provide a novel proof of Chu’s two partial fraction decompositions.
N. Boonsatit, , R. Sriraman, C. P. Lim, P. Agarwal
Advances in Difference Equations, Volume 2021, pp 1-25; doi:10.1186/s13662-021-03438-1

Abstract:
This paper investigates the problem of finite-/fixed-time synchronization for Clifford-valued recurrent neural networks with time-varying delays. The considered Clifford-valued drive and response system models are firstly decomposed into real-valued drive and response system models in order to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers. Then, suitable time-delayed feedback controllers are devised to investigate the synchronization problem in finite-/fixed-time of error system. On the basis of new Lyapunov–Krasovskii functional and new computational techniques, finite-/fixed-time synchronization criteria are formulated for the corresponding real-valued drive and response system models. Two numerical examples demonstrate the effectiveness of the theoretical results.
Assane Savadogo, Boureima Sangaré, Hamidou Ouedraogo
Advances in Difference Equations, Volume 2021, pp 1-23; doi:10.1186/s13662-021-03437-2

Abstract:
In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.
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