[PDF] Top 20 Existence and attractivity of solutions for fractional difference equations

... decade, fractional differential equations have been recognized as valuable tools to describe many phenomena in various fields of engineering, physics, science, and so ...on fractional differential ... See full document

... the existence and attractivity of global solutions for a class of nonlinear fractional integral equations and fractional differential equations in a Banach space X, ... See full document

... using cone theory, they then deduced the existence of one or more positive solutions. Of particular interest with regard to the present paper is the recent work by Benchohra et al. []. In that paper, the ... See full document

... 1. Abdeljawad, T: On Riemann and Caputo fractional differences. Appl. Comput. Math. 62, 1602-1611 (2011) 2. Holm, M: Sum and difference compositions in discrete fractional calculus. CUBO 13(3), 153-184 (2011) ... See full document

... 18. Gray, H.L., Zhang, N.F.: On a new definition of the fractional difference. Math. Comput. 50(182), 513–529 (1988) 19. Atici, F.M., Eloe, P.W.: A transform method in discrete fractional calculus. Int. J. ... See full document

... the existence of positive ...lower solutions method and the Schauder fixed point theorem, and we obtain sufficient conditions so that the problem has at least one positive solution, two positive ... See full document

... of fractional stochastic impulsive neutral functional differential equations with infinite delay which arise from many practical applications such as viscoelasticity and ...Using fractional ... See full document

... differential equations are of interest in many areas of applications, such as eco- nomics, signal identification and image processing, optical systems, aerodynamics, bio- physics, thermal system materials and ... See full document

... where A, B : D × D → E are two nonlinear operators, D is a subset of E. There have ap- peared a series of research results concerning the nonlinear operator equation x = A(x, x) and x = Ax (see, for example, [37]) or the ... See full document

... It is easy to see that y = y(t) is a solution of the FBVP () if and only if y = y(t) is a fixed point of T . We shall obtain sufficient conditions for the existence of fixed points of T. First, we notice that T is a ... See full document

... the existence and uniqueness of single positives solutions to the three-point boundary value problem ...the existence of multiple positives solutions for ... See full document

... the existence of periodic solutions, subharmonic solutions, and homoclinic solutions of some special forms of ...periodic solutions for difference ...the existence of homoclinic ... See full document

... 1. Diethelm, K., Freed, A.D.: On the solution of nonlinear fractional order differential equations used in the modelling of viscoplasticty. In: Keil, F., Mackens, W., Voss, H., Werther, J. (eds.) Scientific ... See full document

... [26] J. Liang and T-J. Xiao, “Solvability of the Cauchy problems for infinite delay equations”, Nonlinear Analysis: Theory, Methods & Applications, vol.58, no.3-4, 2004, pp.271-297. [27] A.Pazy, Semigroups of ... See full document

... Existence of Positive Solutions to Semipositone Fractional Differential Equations Xinsheng Du School of Mathematics Sciences, Qufu Normal University, Qufu, China Received 19 June 2016; a[r] ... See full document

... of fractional dif- ferential equations which has played an important role in different areas of science (see for example, [–] and the references ...of fractional differential equations in ... See full document

... Proof From the proof of Theorem ., we see that (.) has a positive solution u(t) with r ≤ u ≤ R, and by Theorem ., we see that (.) has another positive solution u(t) with  < u < r. Thus (.) has at least ... See full document

... The rest of this paper is organized as follows. In Section , we give some necessary nota- tions, definitions, and lemmas. In Section , we study the existence of solutions of (.) by the coincidence degree ... See full document

... of fractional differential equations with Riemann–Stieltjes integral ...The existence and uniqueness of nontrivial solutions to the above system are established under some weaker conditions by ... See full document

... the existence of the fractional finite difference equation (FFDE) μ μ –2 x(t) = g(t + μ – 1, x(t + μ – 1), x(t + μ – 1)) via the boundary condition x( μ – 2) = 0 and the sum boundary condition x( μ + b + 1) = ... See full document