Nonlinear Analysis: Modelling and Control
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Fractal perspective on dynamics of dark matter and dark energy interactions
Full text linkIn this paper, the dynamics of intricate chaotic attractors of the nonlinear system modeling the dark matter and dark energy interactions is studied indulging fractal–fractional operator in the Caputo sense. The constructed strange attractors witness that the dynamics of the universe components is dominated by the fractal properties. The fractional entropies stemmed from the classical entropy are estimated with fractal parameter and graphically portrayed to measure the randomness of the dynamic variables associated with the proposed dynamical system
Fractional elliptic obstacle systems with multivalued terms and nonlocal operators
Full text linkIn this paper, we introduce and study a fractional elliptic obstacle system, which is composed of two elliptic inclusions with fractional (pi, qi)-Laplace operators, nonlocal functions, and multivalued terms. The weak solution of fractional elliptic obstacle system is formulated by a fully nonlinear coupled system driven by two nonlinear and nonmonotone variational inequalities with constraints. The nonemptiness and compactness of solution set in the weak sense are proved via employing a surjectivity theorem to the multivalued operators formulated by the sum of a multivalued pseudomonotone operator and a maximal monotone operator
Controllability of psi-Hilfer fractional differential equations with infinite delay via measure of noncompactness
No full textIn this article, we study the controllability of ψ-Hilfer fractional differential equations with infinite delay. Sufficient conditions for controllability results are obtained by using the notion of the measure of noncompactness and the Mönch fixed point theorem. The novel feature of this study is to inquire into the controllability notion by using ψ-Hilfer fractional derivative, the generalized variant of the Hilfer derivative. Finally, we provide a numerical example to illustrate our main result
The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation
Full text linkThe probabilistic cone b-metric space is a novel concept that we describe in this study along with some of its fundamental topological properties and instances. We also established the fixed point theorem for the probabilistic nonlinear Banach contraction mapping on this kind of spaces. Many prior findings in the literature are generalized and unified by our findings. In order to illustrate the basic theorem in ordinary cone b-metric spaces, some related findings are also provided with an application to integral equation
Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model
Full text linkThe continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research
Global threshold analysis of an age-space structured disease model with relapse
Full text linkIn this paper, an age-space structured disease model with age-dependent relapse rate is investigated. We first prove the well-posedness of the model including the existence and uniqueness of the solution, positivity, and boundedness. By performing the Laplace transformation to renewal equation, we derive the next generation operator, whose spectral radius is defined as the basic reproduction number. By checking the distribution of the roots of the characteristic equation, exploring the strong persistence property of the solution and designing the Lyapunov functionals, we establish the local and global dynamics of the model
On the distribution-tail of the product of gamma random variables
Full text linkIn this paper, we consider the product Πn := ∏nk=1 ξk of n independent identically distributed gamma random variables ξ1, ξ2, . . . , ξn. We derive an asymptotic formula for the survival probability P(Πn > x) as x -> ∞ with the first two remaining terms
Positive solutions for Hadamard-type fractional differential equations with nonlocal conditions on an infinite interval
Full text linkThe purpose of this paper is to analyse the local existence and uniqueness of positive solutions for a Hadamard-type fractional differential equation with nonlocal boundary conditions on an infinite interval. The technique used to arrive our results depends on two fixed point theorems of a sum operator in partial ordering Banach spaces. The local existence and uniqueness of positive solution is given, and we can make iterative sequences to approximate the unique positive solution. For the illustration of the main results, we list two concrete examples in the last section
Global dynamics and optimal control of a nonlinear fractional-order cholera model
Full text linkIn this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asymptotic stability of the equilibrium points have been established using appropriate Lyapunov functional. Moreover, a fractional-order control problem is presented, and its analytical solution is derived using Pontryagin’s maximum principle. Also, some graphical visualizations of the theoretical results are provided. It is found that the factional-order derivative only affect the time to reach the stationary states. Sensitivity analysis reveals that by reducing the rates of new recruitment and both the disease transmission rates, it may be possible to reduce the value of the basic reproduction number
Singular p-biharmonic problem with the Hardy potential
Full text linkThe aim of this paper is to study existence results for a singular problem involving the p-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is established. By using the Nehari manifold method, the multiplicity of solutions is proved. An example is also given to illustrate the importance of these results