Article of the Year 2021
Related Fixed Point Theorems in Partially Ordered b-Metric Spaces and Applications to Integral EquationsRead the full article
Abstract and Applied Analysis publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.
Chief Editor, Dr Wong, is an associate professor at Nanyang Technological University, Singapore. Her research interests include differential equations, difference equations, integral equations, and numerical mathematics.
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Computational Technique to Study Analytical Solutions to the Fractional Modified KDV-Zakharov-Kuznetsov Equation
In this article, we study and investigate the analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov-Kuznetsov (mKDV-ZK) equation. We have got new exact solutions of the fractional mKDV-ZK equation by using first integral method; we found new types of hyperbolic solutions and trigonometric solutions by symbolic computation.
Boundary Value Problems for Liénard-Type Equations with Quadratic Dependence on the “Velocity”
The estimates were obtained for the number of solutions for the Neumann and Dirichlet boundary value problems associated with the Liénard equation with a quadratic dependence on the “velocity.” Sabatini’s transformation is used to reduce this equation to a conservative one, which does not contain the derivative of an unknown function. Despite the one-to-one correspondence between the equilibria, the topological structure of the phase portraits of both equations can differ significantly.
On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients
In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. These problems arise in cell growth models with symmetric and asymmetric modes of division. We determine the general solution to the symmetric cell division problem for a certain class of coefficients and establish the convergence of solutions to a large time asymptotic solution. The existence of a steady size distribution (SSD) solution for an asymmetric cell division problem is established and is shown to be the large time-attracting solution for a certain class of coefficients. The rate of convergence of solutions towards the SSD solution is affected by the choice of coefficients and remains unaffected by the asymmetry in cell division. The uniqueness of solutions to the initial boundary value problem is also established.
Coupled Fixed Point Theorems in Topological Spaces with Size Function Topology
Regarding the concept of size function topology, this allows us to view the topological space as a metric-like space. We prove the existence and uniqueness for a coupled fixed point of the map satisfying some certain contractive conditions.
Discretization Fractional-Order Biological Model with Optimal Harvesting
In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
Projections in Moduli Spaces of the Kleinian Groups
A two-generator Kleinian group can be naturally associated with a discrete group with the generator of order two and where This is useful in studying the geometry of the Kleinian groups since will be discrete only if is, and the moduli space of groups is one complex dimension less. This gives a necessary condition in a simpler space to determine the discreteness of . The dimension reduction here is realised by a projection of principal characters of the two-generator Kleinian groups. In applications, it is important to know that the image of the moduli space of Kleinian groups under this projection is closed and, among other results, we show how this follows from Jørgensen’s results on algebraic convergence.