2009
DOI: 10.1007/s12591-009-0027-5
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On the solutions for impulsive fractional functional differential equations

Abstract: In this paper, the existence, uniqueness and uniform stability of solutions for a class of impulsive fractional functional differential equations are investigated by applying new boundedness condition and Lipschitz condition. An example is given to illustrate the main results.impulse are considered,Denote by P C 1 ([t 0 − τ, b], R n ) the Banach space of all continuous functions from J into R n with the norm x ∞ = sup t∈[t0−τ,b]

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Cited by 21 publications
(4 citation statements)
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“…We find in the literature a vast collection of works dealing with these issues for different fractional derivatives. For example, for the Riemann-Liouville [8][9][10][11][12], the Caputo [13][14][15][16], or the Hadamard [17,18] fractional derivatives.…”
Section: Introductionmentioning
confidence: 99%
“…We find in the literature a vast collection of works dealing with these issues for different fractional derivatives. For example, for the Riemann-Liouville [8][9][10][11][12], the Caputo [13][14][15][16], or the Hadamard [17,18] fractional derivatives.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional Calculus is a new powerful tool which has been recently employed to model complex biological systems with non-linear behavior and long-term memory. In recent years, there has been a significant development in fractional differential equations involving fractional derivatives, see the monographs of [1][2][3][4][5] and [6][7][8]. In Refs.…”
Section: Introductionmentioning
confidence: 99%
“…Additionally, in relation to the mathematical simulation in chaos, fluid dynamics, and many physical systems, recently the investigation of impulsive fractional functional differential equations began. Fractional-order impulsive functional differential equations are found to be more adequate than integer-order models in many applications and real-world phenomena studying in physics, mechanics, chemistry, engineering, and finance [15][16][17][18].…”
Section: Introductionmentioning
confidence: 99%