Narrow Results

In this paper, we use Krasnoselskii’s fixed point theorem to find existence results for the solution of the following nonlinear fractional differential equations (FDEs) for a coupled system involving AB-Caputo fractional derivative

In this research paper, we find the numerical solutions of fractional order scalers and coupled system of differential equations under initial conditions using shifted Legendre polynomials. By using the properties of shifted Legendre polynomials, we establish operational matrices of integration and differentiation in order to simplify our considered problems under initial conditions. In order to check the accuracy of the proposed model, some test problems are solved along with the graphical representations. For coupled system, we applied the algorithm to the Pharmacokinetic two-compartment model. As the proposed method is computer-oriented, we use therefore the MATLAB for required calculations. Numerical results are shown graphically.

In this paper, we introduce a coupled system of nonlocal fractional q-integro-differential equations. Under certain assumptions, we prove the existence and uniqueness of solutions for a coupled system of fractional q-integro-differential equations. We also study continuous dependence. We solve this system numerically using the finite–Simpson’s and cubic spline–Simpson’s methods. Finally, three examples are provided to demonstrate the efficacy of the methods employed.

We study the collective behavior of populations, coupling the equilibrium and chaotic subsystems by mutual migration. It is assumed that the dynamics of an isolated subsystem is modeled by the Ricker map, and the intensity of migrations within the metapopulation is subject to random perturbations. In the deterministic case, we specify parameter zones of mono- and birhythmicity with regular and chaotic attractors. Noise-induced multistage transitions from order to chaos and vice versa are investigated from an approach that combines direct numerical simulations, studies of chaotic transients, stochastic sensitivity, and confidence domains.

This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection. The results focus on showing regularity, existence and uniqueness of weak solutions using the condition of a nonlinear slightly positive parabolic operator and the reaction-absorption monotone properties. The coupling in the reaction-absorption terms, that characterizes the species interaction, impedes the formulation of a global comparison principle that is shown to exist locally. Additionally, this work provides analytical solutions obtained as selfsimilar minimal and maximal profiles. A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive. When the desertion of the invaded starts, the diffusive front vanishes globally and the nonlinear diffusion concentrates only on the propagating tail which exhibits finite speed. Finally, the invaded specie is shown to exhibit an exponential decay along a characteristic curve. Such exponential decay is not trivial in the nonlinear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.

The main purpose of this paper is to compute all irreducible spherical functions on of arbitrary type , where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space ℍ = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of H in terms of Gauss' functions ₂F₁. Just as in the compact instance treated in [7], there is a useful role for a special class of generalized hypergeometric functions _p+1 F_p.

In this paper, we investigate a nonlinear coupled system of fractional pantograph differential equations (FPDEs). The respective results address some adequate results for existence and uniqueness of solution to the problem under consideration. In light of fixed point theorems like Banach and Krasnoselskii’s, we establish the required results. Considering the tools of nonlinear analysis, we develop some results regarding Ulam–Hyers (UH) stability. We give three pertinent examples to demonstrate our main work.

This note concerns the paper "On the controllability of a coupled system of two Korteweg–de Vries equations" by Micu et al. [2]. They study a nonlinear coupled system of two Korteweg–de Vries equations and prove that the system is controllable by using four boundary controls. Here, we prove that in some cases it is possible to get the controllablity of the system by using only two controls. This can be done depending on both the spatial domain and the control time.

In this paper, we are concerned with the problem of existence of a capacity solution to the strongly nonlinear degenerate problem, namely, $\frac{\partial 𝜃}{\partial t}+H(𝜃)=\sigma (𝜃)|\nabla \psi {|}^2,div(\sigma (𝜃)\nabla \psi )=0$ in $Q$, where the operator $H$ is of the form