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Wu, Guo-Cheng; Zeng, De-Qiang; Baleanu, Dumitru

Fractional impulsive differential equations: exact solutions, integral equations and short memory case. (English) Zbl 1428.34025

Fract. Calc. Appl. Anal. 22, No. 1, 180-192 (2019).
Summary: Fractional impulsive differential equations are revisited first. Some fundamental solutions of linear cases are given in this study. One straightforward technique without using integral equation is adopted to obtain exact solutions which are given by use of piecewise functions. Furthermore, a class of short memory fractional differential equations is proposed and the variable case is discussed. Mittag-Leffler solutions with impulses are derived which both satisfy the equations and impulsive conditions, respectively.

Cited in 48 Documents

MSC:

34A08 Fractional ordinary differential equations
34A37 Ordinary differential equations with impulses
34A05 Explicit solutions, first integrals of ordinary differential equations
34A30 Linear ordinary differential equations and systems

Keywords:

fractional calculus; variable order; short memory; impulsive fractional differential equations
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