Stability in higher-order nonlinear fractional differential equations

We give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of higher-order nonlinear fractional differential equations. By using Krasnoselskii's xed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided that f (t, 0) = 0. The results obtained here generalize the work of Ge and Kou

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR FRACTIONAL RELAXATION INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS

The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation integro-differential equations with boundary conditions. Some results about the existence and uniqueness of solutions are established by using the Banach contraction mapping principle and the Schauder fixed point theorem. An example is provided which illustrates the theoretical results

ASYMPTOTIC STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

In this paper, we study the asymptotic stability of a generalized nonlinear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton b5, Zhang z, Dib, Maroun and Raffoul d1, and Ardjouni and Djoudi a2.1. An example is also given to illustrate our results

Periodic solutions for a second order nonlinear neutral functional differential equation with variable delay

In this paper we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay. We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show that, under suitable conditions, such maps fit very nicely into the framework of Krasnoselskii-Burton's fixed point theorem so that the existence of periodic solutions is concluded

APPROXIMATING SOLUTIONS OF NONLINEAR HYBRID CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS VIA DHAGE ITERATION PRINCIPLE

In this article, we prove the existence and approximation of solutions of the initial value problems of nonlinear hybrid Caputo fractional integro-differential equations. The main tool employed here is the Dhage iteration principle in a partially ordered normed linear space. An example is also given to illustrate the main results

EXISTENCE AND EXPONENTIAL STABILITY OF POSITIVE PERIODIC SOLUTIONS FOR SECOND-ORDER DYNAMIC EQUATIONS

In this article, we establish the existence of positive periodic solutions for second-order dynamic equations on time scales. The main method used here is the Schauder fixed point theorem. The exponential stability of positive periodic solutions is also studied. The results obtained here extend some results in the literature. An example is also given to illustrate this work

NONLINEAR NEUTRAL CAPUTO-FRACTIONAL DIFFERENCE EQUATIONS WITH APPLICATIONS TO LOTKA-VOLTERRA NEUTRAL MODEL

In this paper, we consider a nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of solutions is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in Azabut

Kapasitas Adaptif Mangrove pada Pulau Kecil Mikro Studi di Pulau Maitara Kota Tidore Kepulauan Propinsi Maluku Utara

Mangrove adalah ekosistem pesisir transisi yang unik, tumbuh diantara lingkungan laut dan terestrial, penyebaran umumnya terbatas pada daerah tropis dan subtropis di seluruh dunia.Menyediakan berbagai layanan ekologi, ekonomi serta sosial.Efektif berfungsi sebagai pelindung lahan daratan pesisir pulau kecil.The purpose of this study is to determine the adaptive capacity of mangrove ecosystems on Maitara Island.Penelitian ini dilakukan dengan metodePengukuran Kapasitas Adaptif Ekosistem Mangrove.Hasil penelitian ini ditemukan sebanyak 4 spesies mangrove yaitu, Rhizophora apiculata,R. mucronata, R. stylosa danSoneratia alba, terdiri dari 2 genera,Rhizophora, dan Sonneratia.Nilai indeks dominasi sebesar 0,57, dominasi sedang oleh R. apiculata.Kerapatan pohon per hektar sebanyak 789 tegakan.Nilai kapasitas adaptif ekosistem mangrove di pulau Maitara sebesar 0,44, yang berarti bahwa kapastias adaptif mangrove pulau tersebut“sedang”

Positive periodic solutions of second-order nonlinear neutral differential equations with variable coefficients

In this paper, we use Krasnoselskii's fixed point theorem to establish the existence of positive periodic solutions of second-order nonlinear neutral differential equations. Our techniques can be used and applied to study other classes of problems and extension some results