• Title, Summary, Keyword: impulsive differential equations

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A NOTE ON EXPLICIT SOLUTIONS OF CERTAIN IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS

  • Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.30 no.1
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    • pp.159-164
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    • 2017
  • This paper deals with linear impulsive differential equations involving the Caputo fractional derivative. We provide exact solutions of nonhomogeneous linear impulsive fractional differential equations with constant coefficients by means of the Mittag-Leffler functions.

ON EXACT SOLUTIONS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH NON-INTEGER ORDERS

  • Choi, Sung Kyu;Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.515-521
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    • 2016
  • This paper deals with linear impulsive differential equations with non-integer orders. We provide the explicit representation of solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions.

A NOTE ON LINEAR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS

  • Choi, Sung Kyu;Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.4
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    • pp.583-590
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    • 2015
  • This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.

STABILITY PROPERTIES IN IMPULSIVE DIFFERENTIAL SYSTEMS OF NON-INTEGER ORDER

  • Kang, Bowon;Koo, Namjip
    • Journal of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.127-147
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    • 2019
  • In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS

  • Lan, Heng-You
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.111-123
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    • 2008
  • In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

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