Filippov’s Theorem for Impulsive Differential Inclusions with Fractional Order
نویسندگان
چکیده
In this paper, we present an impulsive version of Filippov’s Theorem for fractional differential inclusions of the form: D ∗ y(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, α ∈ (1, 2], y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, . . . ,m, y(t+k )− y (t−k ) = Ik(y (t−k )), k = 1, . . . ,m, y(0) = a, y′(0) = c, where J = [0, b], D ∗ denotes the Caputo fractional derivative and F is a setvalued map. The functions Ik, Ik characterize the jump of the solutions at impulse points tk (k = 1, . . . ,m).
منابع مشابه
Some results on impulsive boundary value problem for fractional differential inclusions
This paper deals with impulsive fractional differential inclusions with a fractional order multi-point boundary condition and with fractional order impulses. By use of multi-valued analysis and topological fixed point theory, we present some existence results under both convexity and nonconvexity conditions on the multi-valued right-hand side. The compactness of the solutions set and continuous...
متن کاملStructure of Solutions Sets and a Continuous Version of Filippov’s Theorem for First Order Impulsive Differential Inclusions with Periodic Conditions
In this paper, the authors consider the first-order nonresonance impulsive differential inclusion with periodic conditions y′(t)− λy(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, 2, . . . ,m, y(0) = y(b), where J = [0, b] and F : J × R → P(R) is a set-valued map. The functions Ik characterize the jump of the solutions at impulse points tk (k = 1, 2, ....
متن کاملSuppressing chaos in discontinuous systems of fractional order by active control
In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov’s convex regularization and via differential inclusions, the underlying discontinuous initial value problem is first recast in terms of a set-valued problem and hence it is continuously approximated by using Cellina’s Theor...
متن کاملExistence of Solutions for Fractional-Order Neutral Differential Inclusions with Impulsive and Nonlocal Conditions
This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example...
متن کاملExistence of Solutions to Fractional-order Impulsive Hyperbolic Partial Differential Inclusions
In this article we use the upper and lower solution method combined with a fixed point theorem for condensing multivalued maps, due to Martelli, to study the existence of solutions to impulsive partial hyperbolic differential inclusions at fixed instants of impulse.
متن کامل