Periodic solutions of fractional differential equations with delay

Abstract

Artículo de publicación ISIIn this paper, we give a necessary and sufficient conditions for the existence and uniqueness of periodic solutions of inhomogeneous abstract fractional differential equations with delay. The conditions are obtained in terms of R-boundedness of operator-valued Fourier multipliers determined by the abstract model.FONDECYT 1100485 FONDECYT de Iniciacion 1107504

Well-Posedness of Fractional Differential Equations on Vector-Valued Function Spaces

“…It is clear that the definition (2.3) coincides with the definition (2.1) when α = 1, and D = D 1 . See [18] for an equivalent definition of the fractional derivative D α on L p (T, X).…”

“…[1][2][3]8,[10][11][12][13][14][15][16][17][18]20,21]). They are useful in the study of the well-posedness of differential equations on Banach spaces.…”

“…was recently studied by Lizama and Poblete, they have completely characterized the well-posedness of (P 3 ) on L p (T, X) and B s p,q (T, X) [18]. Our main tool in the study of the well-posedness of (P 2 ) is operator-valued Fourier multiplier.…”

Symmetric-periodic solutions for some types of generalized neutral equations

“…The existence of periodic solutions is often a desired property in dynamical systems, constituting one of the most important research directions in the theory of dynamical systems, with applications ranging from celestial mechanics to biology and finance. Fractional differential equations (FDEs) are the most important generalizations of the field of ODE [17][18][19][20][21]. Recent investigations in physics, engineering, biological sciences and other fields have demonstrated that the dynamics of many systems are described more accurately using FDEs, and that FDE with delay are often more realistic to describe natural phenomena than those without delay.…”

“…Periodic solution fractional differential equations have been studied by many researchers. They studied periodic solutions of the equation (see [17,18])…”