Non-instantaneous impulses in caputo fractional differential equations
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Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal (2017). Non-instantaneous impulses in caputo fractional differential equations. Fractional Calculus and Applied Analysis 20 (3), 595-622
Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.