Existence and uniqueness of mild solutions to impulsive fractional differential equations

UPPER AND LOWER SOLUTION METHOD FOR FRACTIONAL EVOLUTION EQUATIONS WITH ORDER 1 < α < 2

“…In order to evaluate the behaviors of fractional order differential equation based models, one need to know the properties of such equation systems, in particular, the existence of solutions to such equations. Recently, the existence of solutions to different forms of fractional differential equation systems has been investigated [1,2,3,4,5,9,10,11,15,16,19,20,21,23,26,27,29,30,32,33,34].…”

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

“…Many physical processes appear to exhibit fractional order behavior that may vary with time or space. In recent years, there has been a significant development in ordinary and partial differential equations involving fractional derivatives; we only enumerate here the monographs of Kilbas et al [26,27], Diethelm [28], Hilfer [29], Podlubny [30], Miller [31], and Zhou [32] and the papers of Agarwal et al [33,34], Benchohra et al [35,36], El-Borai [37], Lakshmikantham et al [38][39][40][41], Mophou et al [42][43][44][45], N'Guérékata [46], and Zhou et al [47][48][49][50] and the reference therein.…”

New results for fractional differential equations with impulses via variational methods

“…The governing equations of such phenomena may be modeled as impulsive differential equations. In recent years, there has been a growing interest in the study of impulsive differential equations as these equations provide a natural framework for mathematical modeling of many real world phenomena, namely in the control theory, physics, chemistry, population dynamics, biotechnology, economics, and medical fields [17,21].…”