We consider a saturated predator-prey system with delayed time. The system is motivated by natural disease management using the interactions between the original and the treated species populations, such as Aedes aegypti and Wolbachia mosquitoes, fertile and infertile pests as a pesticide&#x2019;s effect, uninfected and infected cancer cells by an oncolytic virus, and so forth. The delayed time shows the gestation effect of the treated populations where the impact on the stability of the unique positive equilibrium point of the system will be studied. We obtain the exact formula of the equilibrium point where it is asymptotically stable for the nondelay case. The stability region of the nonzero solution is given in parameter space following the Pontryagin criteria. Furthermore, some conditions, such that for delay case this solution is conditionally stable, are also provided in this study.

Nikenasih Binatari

Fajar Adi-Kusumo

Lina Aryati

Stability Regions and Bifurcation Analysis of a Delayed Predator-Prey Model Caused from Gestation Period

In this paper, we establish the solution of the fourth-order nonlinear homogeneous neutral functional difference equation. Moreover, we study the new oscillation criteria have been established which generalize some of the existing results of the fourth-order nonlinear homogeneous neutral functional difference equation in the literature. Likewise, a few models are given to represent the significance of the primary outcomes.

G. Sumitha

R. Kodeeswaran

S. Noeiaghdam

S. Balamuralitharan

V. Govindan

Oscillation of Fourth-Order Nonlinear Homogeneous Neutral Difference Equation

In this work, we prove the existence and uniqueness of mild solution of the fractional conformable Cauchy problem with nonlocal condition. We obtained these results by applying the fixed point theorems precisely to the fixed point theorem of Krasnoselskii and Banach&#x2019;s fixed point theorem. At the end, we provide application.

Khalid Hilal

Ahmed Kajouni

Najat Chefnaj

Existence of Solution for a Conformable Fractional Cauchy Problem with Nonlocal Condition

In this work, we discuss the existence and uniqueness of solution for a boundary value problem for the Langevin equation and inclusion with the Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Second of all, we give our first existence result, based on Krasnoselskii&#x2019;s fixed point, and to deal with the uniqueness result, we use Banach&#x2019;s contraction principle. Third of all, in the inclusion case, to obtain the existence result, we use the Leray&#x2013;Schauder alternative. Last but not least, we give an illustrative example.

Hamid Lmou

Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative

In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Sch&#xe4;fer&#x2019;s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.

Khaled Bouazzaoui

Mohammed Aiboudi

Sameh Elsayed Ahmed

Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow

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International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

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International Journal of Differential Equations | Hindawi

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International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

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International Journal of Differential Equations

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International Journal of Differential Equations