Impulsive differential inclusions with fractional order

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}, (1, 2], y(t+ k ) - y(tk ) = Ik(y(tk )), k = 1, . . . , m, y(t+ k ) - y(tk ) = Ik(y(tk )), 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). Key words and phrases: Fractional differential inclusions, fractional derivative, fractional integral. AMS (MOS) Subject Classifications: 34A60, 34A37.

• Type: Journal
• Year: 2010
• Where: CMA
• Authors: Johnny Henderson, Abdelghani Ouahab
• Keywords: CMA 2010, Fractional Derivative, Fractional Integral, Impulsive Version