[PDF] Top 20 Stability and asymptotic properties of a linear fractional difference equation

... tion, basic properties and general information about the continuous fractional calculus we refer, e.g. to []). It is well known that solutions x(t) of (.) with  < α <  are unbounded in a right ... See full document

... has been investigated in [9]. Here we will obtain more precise results for the special case of system (1.1) by using the monotonicity properties of the map in (1.1). We will give some basic results on the ... See full document

... which is of the form (1.1). In [12] we showed that in cases (1)–(3) the introduction of the positive parameters a and d creates a unique positive equilibrium which is globally asymptotically stable, and so the principle ... See full document

... The primary goal of this paper does not consist in the generalization of these results. Although we are going to formulate the asymptotic bound of solutions for a system of the general form 1.1, we show that ... See full document

... uniform asymptotic stability of the zero solution of ...three properties without such restrictive conditions; more precisely, we have established the ... See full document

... nonlinear equation instead of a rational difference equation one ...nonlinear difference equations of order greater than ...qualitative properties of nonlinear difference ... See full document

... local asymptotic stability of the equilibrium point of Equation ...global asymptotic stability behavior was used, like the idea in ...the stability was examined that depends on ... See full document

... Caputo’s fractional deriva- tive; we use the central difference to approximate both the first and second space deriva- tive; we use the linear difference to approximate the nonlinear term; and we use the ... See full document

... in fractional calculus and applied them to study the qualitative and quantitative properties of fractional difference equations ...of stability of fractional differential as well as ... See full document

... the linear di ff erence equation is asymptotically stable if and only if all the roots of its associated characteristic equation are inside the unit ...the asymptotic sta- bility of ... See full document

... to stability, the pass initial conditions are completely ...(2), stability in this sense depends on both and whereas asymptotic stability (Theorem 1) from the abstract model based theory only ... See full document

... This paper is an attempt at establishing some global stability results for the equilibrium solution(s) of Eq. (). Our results give effective conditions for global asymptotic stabil- ity of the equilibrium ... See full document

... differential equation, difference equations have applications in various scientific branches such as biology, ecology, physiology, physics, engineering and economics, ...globally asymptotic behavior ... See full document

... for any > . It is clear that the solution x(t) does not converge to the zero solution expo- nentially; that is, the zero solution is not exponentially stable. Here, the first question of this paper arises. Will ... See full document

... 7. Oyedepo T, Taiwo OA, Abubakar JU, Ogunwobi ZO (2016) “Numerical Studies for Solving Fractional Integro-Differential Equations by using Least Squares Method and Bernstein Polynomials”. Fluid Mech Open Acc 3: ... See full document

... operator. To the best of our knowledge, this is a pioneering work on discussing initial value problems IVP for short in discrete fractional calculus. Anastassiou 4 defined a Caputo like discrete fractional ... See full document

... It is important to note that many nonlinear difference equations and systems can be reduced to some special cases of equation (), which means that they are solvable too. Some interest in the area has been renewed ... See full document

... Kaewong: Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand E-mail address: [email protected] Y.. Lenbury: Department of Mathematics, Fac[r] ... See full document

... [5] X. Yang, D. J. Evans, and G. M. Megson, “Global asymptotic stability in a class of Putnam-type equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 1, pp. 42–50, 2006. [6] J. ... See full document

... the asymptotic theory of the solutions of Volterra difference equations is extensive, and application of this theory is rapidly increasing to various ...the asymptotic theory of difference equations is given ... See full document